@misc{19769, abstract = {Artifact to reproduce the experimental results presented in the article "Sound Statistical Model Checking for Probabilities and Expected Rewards" by Carlos E. Budde, Arnd Hartmanns, Tobias Meggendorfer, Maximilian Weininger, and Patrick Wienhöft (TACAS 2025). The contents include all data and software (formal models, software tools, Python & bash scripts) used in the experimental evaluation presented in sections 3, 4, and 6 of the article. Detailed instructions on how to reproduce the results are bundled in the artifact.}, author = {Budde, Carlos and Hartmanns, Arnd and Meggendorfer, Tobias and Weininger, Maximilian and Wienhöft, Patrick}, publisher = {Zenodo}, title = {{Sound statistical model checking for probabilities and expected rewards (experimental reproduction package)}}, doi = {10.5281/ZENODO.14602066}, year = {2025}, } @article{19965, abstract = {Multiagent learning is challenging when agents face mixed-motivation interactions, where conflicts of interest arise as agents independently try to optimize their respective outcomes. Recent advancements in evolutionary game theory have identified a class of “zero-determinant” strategies, which confer an agent with significant unilateral control over outcomes in repeated games. Building on these insights, we present a comprehensive generalization of zero-determinant strategies to stochastic games, encompassing dynamic environments. We propose an algorithm that allows an agent to discover strategies enforcing predetermined linear (or approximately linear) payoff relationships. Of particular interest is the relationship in which both payoffs are equal, which serves as a proxy for fairness in symmetric games. We demonstrate that an agent can discover strategies enforcing such relationships through experience alone, without coordinating with an opponent. In finding and using such a strategy, an agent (“enforcer”) can incentivize optimal and equitable outcomes, circumventing potential exploitation. In particular, from the opponent’s viewpoint, the enforcer transforms a mixed-motivation problem into a cooperative problem, paving the way for more collaboration and fairness in multiagent systems.}, author = {Mcavoy, Alex and Sehwag, Udari Madhushani and Hilbe, Christian and Chatterjee, Krishnendu and Barfuss, Wolfram and Su, Qi and Leonard, Naomi Ehrich and Plotkin, Joshua B.}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {25}, publisher = {National Academy of Sciences}, title = {{Unilateral incentive alignment in two-agent stochastic games}}, doi = {10.1073/pnas.2319927121}, volume = {122}, year = {2025}, } @inproceedings{20053, abstract = {Liquid democracy is a transitive vote delegation mechanism over voting graphs. It enables each voter to delegate their vote(s) to another better-informed voter, with the goal of collectively making a better decision. The question of whether liquid democracy outperforms direct voting has been previously studied in the context of local delegation mechanisms (where voters can only delegate to someone in their neighbourhood) and binary decision problems. It has previously been shown that it is impossible for local delegation mechanisms to outperform direct voting in general graphs. This raises the question: for which classes of graphs do local delegation mechanisms yield good results? In this work, we analyse (1) properties of specific graphs and (2) properties of local delegation mechanisms on these graphs, determining where local delegation actually outperforms direct voting. We show that a critical graph property enabling liquid democracy is that the voting outcome of local delegation mechanisms preserves a sufficient amount of variance, thereby avoiding situations where delegation falls behind direct voting1. These insights allow us to prove our main results, namely that there exist local delegation mechanisms that perform no worse and in fact quantitatively better than direct voting in natural graph topologies like complete, random d-regular, and bounded degree graphs, lending a more nuanced perspective to previous impossibility results.}, author = {Chatterjee, Krishnendu and Gilbert, Seth and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {Proceedings of the ACM Symposium on Principles of Distributed Computing}, isbn = {9798400718854}, location = {Huatulco, Mexico}, pages = {241--251}, publisher = {Association for Computing Machinery}, title = {{When is liquid democracy possible?: On the manipulation of variance}}, doi = {10.1145/3732772.3733544}, year = {2025}, } @article{20254, abstract = {We examine population structures for their ability to maintain diversity in neutral evolution. We use the general framework of evolutionary graph theory and consider birth–death (bd) and death–birth (db) updating. The population is of size N. Initially all individuals represent different types. The basic question is: what is the time TN until one type takes over the population? This time is known as consensus time in computer science and as total coalescent time in evolutionary biology. For the complete graph, it is known that TN is quadratic in N for db and bd. For the cycle, we prove that TN is cubic in N for db and bd. For the star, we prove that TN is cubic for bd and quasilinear (N log N) for db. For the double star, we show that TN is quartic for bd. We derive upper and lower bounds for all undirected graphs for bd and db. We also show the Pareto front of graphs (of size N = 8) that maintain diversity the longest for bd and db. Further, we show that some graphs that quickly homogenize can maintain high levels of diversity longer than graphs that slowly homogenize. For directed graphs, we give simple contracting star-like structures that have superexponential time scales for maintaining diversity.}, author = {Brewster, David A. and Svoboda, Jakub and Roscow, Dylan and Chatterjee, Krishnendu and Tkadlec, Josef and Nowak, Martin A.}, issn = {2752-6542}, journal = {PNAS Nexus}, number = {8}, publisher = {Oxford University Press}, title = {{Maintaining diversity in structured populations}}, doi = {10.1093/pnasnexus/pgaf252}, volume = {4}, year = {2025}, } @inproceedings{20610, abstract = {Markov decision processes (MDPs) are a fundamental model of decision making which exhibit non-deterministic choice as well as probabilistic uncertainty. Traditionally, verification assumes exact knowledge of the probabilities that govern the behaviour of an MDP. However, this assumption often is unrealistic, e.g. when modelling cyber-physical systems or biological processes. There, we can employ statistical model checking (SMC) to obtain an estimate of the MDP’s value (e.g. the maximal probability of reaching a goal state) that is close to the true value with high confidence (probably approximately correct). Model-based SMC algorithms sample the MDP and build a model of it by estimating all transition probabilities, essentially for every transition answering the question: “What are the odds?” However, so far the statistical methods employed by state-of-the-art SMC verification algorithms are quite naive or even compromise the correctness guarantees. Our first contribution is to survey, categorize, and analyse statistical methods, identifying those few that are most efficient and that provide suitable guarantees for the verification setting. Secondly, we propose improvements that exploit structural knowledge of the MDP. Both contributions generalize to many types of problem statements as they are largely independent of the setting. Moreover, our experimental evaluation shows that they lead to significant gains, reducing the number of samples that an SMC algorithm has to collect by up to two orders of magnitude.}, author = {Meggendorfer, Tobias and Weininger, Maximilian and Wienhöft, Patrick}, booktitle = {Second International Joint Conference on QEST+FORMATS}, isbn = {9783032057914}, issn = {1611-3349}, location = {Aarhus, Denmark}, pages = {195--218}, publisher = {Springer Nature}, title = {{What are the odds? Improving statistical model checking of Markov decision processes}}, doi = {10.1007/978-3-032-05792-1_11}, volume = {16143}, year = {2025}, } @inproceedings{20688, abstract = {We consider two-player zero-sum concurrent stochastic games (CSGs) played on graphs with reachability and safety objectives. These include degenerate classes such as Markov decision processes or turn-based stochastic games, which can be solved by linear or quadratic programming; however, in practice, value iteration (VI) outperforms the other approaches and is the most implemented method. Similarly, for CSGs, this practical performance makes VI an attractive alternative to the standard theoretical solution via the existential theory of reals.VI starts with an under-approximation of the sought values for each state and iteratively updates them, traditionally terminating once two consecutive approximations are ϵ-close. However, this stopping criterion lacks guarantees on the precision of the approximation, which is the goal of this work. We provide bounded (a.k.a. interval) VI for CSGs: it complements standard VI with a converging sequence of over-approximations and terminates once the over- and under-approximations are ϵ-close.}, author = {Grobelna, Marta and Kretinsky, Jan and Weininger, Maximilian}, booktitle = {2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science}, location = {Singapore, Singapore}, pages = {568--580}, publisher = {IEEE}, title = {{Stopping criteria for value iteration on concurrent stochastic reachability and safety games}}, doi = {10.1109/lics65433.2025.00049}, year = {2025}, } @inproceedings{19743, abstract = {The possibility of errors in human-engineered formal verification software, such as model checkers, poses a serious threat to the purpose of these tools. An established approach to mitigate this problem are certificates—lightweight, easy-to-check proofs of the verification results. In this paper, we develop novel certificates for model checking of Markov decision processes (MDPs) with quantitative reachability and expected reward properties. Our approach is conceptually simple and relies almost exclusively on elementary fixed point theory. Our certificates work for arbitrary finite MDPs and can be readily computed with little overhead using standard algorithms. We formalize the soundness of our certificates in Isabelle/HOL and provide a formally verified certificate checker. Moreover, we augment existing algorithms in the probabilistic model checker Storm with the ability to produce certificates and demonstrate practical applicability by conducting the first formal certification of the reference results in the Quantitative Verification Benchmark Set.}, author = {Chatterjee, Krishnendu and Quatmann, Tim and Schäffeler, Maximilian and Weininger, Maximilian and Winkler, Tobias and Zilken, Daniel}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906527}, issn = {1611-3349}, location = {Hamilton, ON, Canada}, pages = {130--151}, publisher = {Springer Nature}, title = {{Fixed point certificates for reachability and expected rewards in MDPs}}, doi = {10.1007/978-3-031-90653-4_7}, volume = {15697}, year = {2025}, } @inproceedings{19740, abstract = {Two standard models for probabilistic systems are Markov chains (MCs) and Markov decision processes (MDPs). Classic objectives for such probabilistic models for control and planning problems are reachability and stochastic shortest path. The widely studied algorithmic approach for these problems is the Value Iteration (VI) algorithm which iteratively applies local updates called Bellman updates. There are many practical approaches for VI in the literature but they all require exponentially many Bellman updates for MCs in the worst case. A preprocessing step is an algorithm that is discrete, graph-theoretical, and requires linear space. An important open question is whether, after a polynomial-time preprocessing, VI can be achieved with sub-exponentially many Bellman updates. In this work, we present a new approach for VI based on guessing values. Our theoretical contributions are twofold. First, for MCs, we present an almost-linear-time preprocessing algorithm after which, along with guessing values, VI requires only subexponentially many Bellman updates. Second, we present an improved analysis of the speed of convergence of VI for MDPs. Finally, we present a practical algorithm for MDPs based on our new approach. Experimental results show that our approach provides a considerable improvement over existing VI-based approaches on several benchmark examples from the literature.}, author = {Chatterjee, Krishnendu and Jafariraviz, Mahdi and Saona Urmeneta, Raimundo J and Svoboda, Jakub}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906527}, issn = {1611-3349}, location = {Hamilton, ON, Canada}, pages = {217--236}, publisher = {Springer Nature}, title = {{Value iteration with guessing for Markov chains and Markov decision processes}}, doi = {10.1007/978-3-031-90653-4_11}, volume = {15697}, year = {2025}, } @inproceedings{19744, abstract = {We consider the problem of refuting equivalence of probabilistic programs, i.e., the problem of proving that two probabilistic programs induce different output distributions. We study this problem in the context of programs with conditioning (i.e., with observe and score statements), where the output distribution is conditioned by the event that all the observe statements along a run evaluate to true, and where the probability densities of different runs may be updated via the score statements. Building on a recent work on programs without conditioning, we present a new equivalence refutation method for programs with conditioning. Our method is based on weighted restarting, a novel transformation of probabilistic programs with conditioning to the output equivalent probabilistic programs without conditioning that we introduce in this work. Our method is the first to be both a) fully automated, and b) providing provably correct answers. We demonstrate the applicability of our method on a set of programs from the probabilistic inference literature.}, author = {Chatterjee, Krishnendu and Kafshdar Goharshadi, Ehsan and Novotný, Petr and Zikelic, Dorde}, booktitle = {31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031906527}, issn = {1611-3349}, location = {Hamilton, ON, Canada}, pages = {279--300}, publisher = {Springer Nature}, title = {{Refuting equivalence in probabilistic programs with conditioning}}, doi = {10.1007/978-3-031-90653-4_14}, volume = {15697}, year = {2025}, } @inproceedings{19667, abstract = {The problem of checking satisfiability of linear real arithmetic (LRA) and non-linear real arithmetic (NRA) formulas has broad applications, in particular, they are at the heart of logic-related applications such as logic for artificial intelligence, program analysis, etc. While there has been much work on checking satisfiability of unquantified LRA and NRA formulas, the problem of checking satisfiability of quantified LRA and NRA formulas remains a significant challenge. The main bottleneck in the existing methods is a computationally expensive quantifier elimination step. In this work, we propose a novel method for efficient quantifier elimination in quantified LRA and NRA formulas. We propose a template-based Skolemization approach, where we automatically synthesize linear/polynomial Skolem functions in order to eliminate quantifiers in the formula. The key technical ingredient in our approach are Positivstellensätze theorems from algebraic geometry, which allow for an efficient manipulation of polynomial inequalities. Our method offers a range of appealing theoretical properties combined with a strong practical performance. On the theory side, our method is sound, semi-complete, and runs in subexponential time and polynomial space, as opposed to existing sound and complete quantifier elimination methods that run in doubly-exponential time and at least exponential space. On the practical side, our experiments show superior performance compared to state of the art SMT solvers in terms of the number of solved instances and runtime, both on LRA and on NRA benchmarks.}, author = {Chatterjee, Krishnendu and Kafshdar Goharshadi, Ehsan and Karrabi, Mehrdad and Motwani, Harshit J. and Seeliger, Maximilian and Zikelic, Dorde}, booktitle = {Proceedings of the 39th AAAI Conference on Artificial Intelligence}, issn = {2374-3468}, location = {Philadelphia, PA, United States}, number = {11}, pages = {11158--11166}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Quantified linear and polynomial arithmetic satisfiability via template-based skolemization}}, doi = {10.1609/aaai.v39i11.33213}, volume = {39}, year = {2025}, } @inproceedings{19669, abstract = {We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability condition; (C2) the non-negative coefficients condition; (C3) the sum upto 1 condition; and (C4) the only min or only max operator condition. Several seminal results in the literature focus on special cases. For example, turn-based stochastic games correspond to conditions C2 and C3; and Markov decision process to conditions C2, C3, and C4. However, the systematic computational complexity study of all the cases has not been explored, which we address in this work. Some highlights of our results are: with conditions C2 and C4, and with conditions C3 and C4, the problem is NP-complete, whereas with condition C1 only, the problem is in UP intersects coUP. Finally, we establish the computational complexity of the decision problem of checking the respective conditions.}, author = {Chatterjee, Krishnendu and Luo, Ruichen and Saona Urmeneta, Raimundo J and Svoboda, Jakub}, booktitle = {Proceedings of the 39th AAAI Conference on Artificial Intelligence}, issn = {2374-3468}, location = {Philadelphia, PA, United States}, number = {11}, pages = {11150--11157}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Linear equations with min and max operators: Computational complexity}}, doi = {10.1609/aaai.v39i11.33212}, volume = {39}, year = {2025}, } @misc{19771, abstract = {This artifact allows to review and reproduce the Isabelle proofs and practical experiments from the paper *Fixed Point Certificates for Reachability and Expected Rewards in MDPs*. The contents are two-fold: First, the artifact contains a formally verified certificate checker for the certificates presented in the paper. The formal Isabelle/HOL proofs of the background theory can be inspected, checked by Isabelle and the code extraction can be retraced. Second, the artifact contains a modified version of the model checking tool `Storm` with support for certificate generation. Together with the provided scripts and benchmark files, this allows to reproduce the experiments from the paper. An appropriate subset of the experiments is given to allow a review in a timely manner. In addition, original logfiles from our experiments are provided, allowing a detailed inspection. The package includes convenient installation scripts for [the TACAS 2023 VM](https://doi.org/10.5281/zenodo.7113223) (based on Ubuntu 22.04). A native installation on Linux or macOS systems (including the newer ARM-based machines) is also possible.}, author = {Chatterjee, Krishnendu and Quatmann, Tim and Schäffeler, Maximilian and Weininger, Maximilian and Winkler, Tobias and Zilken, Daniel}, publisher = {Zenodo}, title = {{Artifact: Fixed point certificates for reachability and expected rewards in MDPs}}, doi = {10.5281/ZENODO.14626585}, year = {2025}, } @phdthesis{19903, abstract = {Cooperation, that is, one person paying a cost for another's benefit, is a fundamental principle without which no form of society could exist. The extent to which humans cooperate with each other is also an essential feature that differentiates them from other animals. Cooperation occurs even in the absence of altruistic motivations, when it is selfishly incentivised by the expectation of a future reward. For example, many economic interactions are well described that way. This kind of cooperation requires that people exhibit reciprocal behaviour that acts as a mechanism that rewards cooperation. With game-theoretic models, it is possible to formally study potential such mechanisms and under what conditions they can exist. This thesis contributes to this effort by analysing recently introduced models of cooperation that advance on previous work by taking into account the potential for pre-existing inequality among cooperating individuals as well as the different forms that reciprocity can take. Individuals may differ both intrinsically, in their abilities, as well as extrinsically, in the amount of resources they have available. Allowing for such differences in a model of cooperation helps to understand how inequality affects the potential for, and outcomes of, cooperation among unequals. In this thesis, it is shown that in the presence of intrinsic inequality, a similar unequal distribution of resources can increase the potential for cooperation. This effect is stronger the smaller the group is in which cooperation takes place. It is also shown that under particular assumptions, if the unequal members of a group vary the size of their contributions to a cooperative effort over time, they can thereby increase their efficiency and improve the collective outcome. Cooperative behaviour in a two-person interaction can be rewarded either by direct reciprocation whenever the same two people interact again, or indirectly by a third party who observed the interaction. In the latter case of indirect reciprocity, individuals are proximally rewarded by a good reputation, which ultimately translates to being rewarded with cooperative behaviour by others. This mechanism can enable selfishly motivated cooperation even in circumstances where individuals are unlikely to meet again, akin to how money facilitates trade. While these two forms of reciprocity have mostly been studied in isolation, this thesis analyses both direct and indirect reciprocity in a general model in order to compare their relative effectiveness under different circumstances. The contribution of this thesis is an extension of previous work regarding a specific kind of interaction, whose parameters allow for convenient mathematical analysis, to the most general set of possible interactions.}, author = {Hübner, Valentin}, issn = {2663-337X}, pages = {157}, publisher = {Institute of Science and Technology Austria}, title = {{Reciprocity and inequality in social dilemmas}}, doi = {10.15479/AT-ISTA-19903}, year = {2025}, } @article{19843, abstract = {Social dilemmas are collective-action problems where individual interests are at odds with group interests. Such dilemmas occur frequently at all scales of human interactions. When dealing with collective-action problems, people often act reciprocally. They adjust their behavior to match the previous behavior of the recipient. The literature distinguishes two kinds of reciprocity. According to direct reciprocity, individuals react to their immediate experiences with the recipient. They are more likely to cooperate if the recipient previously cooperated with them. According to indirect reciprocity, individuals react to the recipient’s general behavior, irrespectively of whether or not they benefited directly. In practice, the two kinds of reciprocity are often intertwined; people typically base their decisions on both direct experiences and indirect observations. Yet only recently have researchers begun to explore how the two kinds of reciprocity interact. So far, this research only addresses a single type of social dilemma, the donation game, where the effects of individual behaviors are independent. Instead, here we allow for all pairwise social dilemmas. By applying novel techniques to generalize the theory of zero-determinant strategies, we establish an important proof of principle: In all social dilemmas, socially optimal outcomes can be sustained as an equilibrium, using either direct or indirect reciprocity, or arbitrary mixtures thereof. These results neither require games to be repeated infinitely often, nor that individual opinions are synchronized. In this way, we considerably generalize the scope of models of reciprocity, and we build further bridges between the literatures on direct and indirect reciprocity.}, author = {Hübner, Valentin and Schmid, Laura and Hilbe, Christian and Chatterjee, Krishnendu}, issn = {2752-6542}, journal = {PNAS Nexus}, number = {5}, publisher = {Oxford University Press}, title = {{Stable strategies of direct and indirect reciprocity across all social dilemmas}}, doi = {10.1093/pnasnexus/pgaf154}, volume = {4}, year = {2025}, } @article{19074, abstract = {The public goods game is among the most studied metaphors of cooperation in groups. In this game, individuals can use their endowments to make contributions towards a good that benefits everyone. Each individual, however, is tempted to free-ride on the contributions of others. Herein, we study repeated public goods games among asymmetric players. Previous work has explored to which extent asymmetry allows for full cooperation, such that players contribute their full endowment each round. However, by design that work focusses on equilibria where individuals make the same contribution each round. Instead, here we consider players whose contributions along the equilibrium path can change from one round to the next. We do so for three different models – one without any budget constraints, one with endowment constraints, and one in which individuals can save their current endowment to be used in subsequent rounds. In each case, we explore two key quantities: the welfare and the resource efficiency that can be achieved in equilibrium. Welfare corresponds to the sum of all players’ payoffs. Resource efficiency relates this welfare to the total contributions made by the players. Compared to constant contribution sequences, we find that time-dependent contributions can improve resource efficiency across all three models. Moreover, they can improve the players’ welfare in the model with savings.}, author = {Hübner, Valentin and Hilbe, Christian and Staab, Manuel and Kleshnina, Maria and Chatterjee, Krishnendu}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {1617--1645}, publisher = {Springer Nature}, title = {{Time-dependent strategies in repeated asymmetric public goods games}}, doi = {10.1007/s13235-025-00627-5}, volume = {15}, year = {2025}, } @phdthesis{20138, abstract = {The evolution shapes the world around us. Not only in biology, where the fittest individuals spread their genes but also in physics and social dynamics, the evolutionary forces determine the development of a state of matter or public opinions. Many models describe these dynamics. This thesis examines the role of the structure in the models of selection. The population structure is represented as a graph or a network, and each vertex is occupied by one individual. Every individual has a type and fitness that represents the reproductive potential and depends on the type, occupied vertex, and the arrangement of the neighbors. The evolution is modeled in discrete steps; in one step, one individual is replaced by a neighbor selected randomly with the influence of fitness. The role of the networks is widely examined in the literature. The structures that promote the spread of the desired type compared to the structureless case are called amplifiers. The existence of amplifiers in various settings is an intensively studied topic, and in some settings, the amplifiers have been identified. Moreover, there are other important questions about the number of steps until one type spreads over the whole network (fixation time), the computational complexity, and the questions about the robustness of these processes. This thesis explores the role of structure in evolution from many perspectives. First, it introduces different models and various choices that can be made in the models of evolution. It highlights the role of the structure in the real world and how this is reflected in these models. Then, it describes the previous results and open problems. Second, the thesis describes an amplifier for two variants of the Moran process: one with a constant birth rate and the other with a constant death rate. This is an important contribution to the robustness of the amplification. Third, the thesis determines the complexity of spatial games. These are processes where the fitness comes from a game, and the strength of selection is high. It shows that determining the fate of cooperation in these games is a PSPACE-complete problem. Fourth, the thesis describes the amplifier of cooperation for spatial games. This is the first amplifier in this setting. Fifth, the thesis examines the coexistence in the Moran process with environmental heterogeneity. In this setting, the fitness depends not only on the type of the individual but also on the occupied vertex. The chapter determines the relationship between the interactions of vertices of different types and the coexistence time. Sixth, the thesis examines the social balance on networks and proposes a stochastic dynamic partially aware of the state of the graph, which reaches a balanced position quickly. Finally, the thesis presents conclusions and outlines the directions for future work. }, author = {Svoboda, Jakub}, issn = {2663-337X}, pages = {167}, publisher = {Institute of Science and Technology Austria}, title = {{Structural properties of games on graphs}}, doi = {10.15479/AT-ISTA-20138}, year = {2025}, } @inproceedings{20299, abstract = {Deterministic Markov Decision Processes (DMDPs) are a mathematical framework for decision-making where the outcomes and future possible actions are deterministically determined by the current action taken. DMDPs can be viewed as a finite directed weighted graph, where in each step, the controller chooses an outgoing edge. An objective is a measurable function on runs (or infinite trajectories) of the DMDP, and the value for an objective is the maximal cumulative reward (or weight) that the controller can guarantee. We consider the classical mean-payoff (aka limit-average) objective, which is a basic and fundamental objective. Howard's policy iteration algorithm is a popular method for solving DMDPs with mean-payoff objectives. Although Howard's algorithm performs well in practice, as experimental studies suggested, the best known upper bound is exponential and the current known lower bound is as follows: For the input size I, the algorithm requires (math formular) iterations, where (math formular) hides the poly-logarithmic factors, i.e., the current lower bound on iterations is sub-linear with respect to the input size. Our main result is an improved lower bound for this fundamental algorithm where we show that for the input size I, the algorithm requires (math formular) iterations.}, author = {Asadi, Ali and Chatterjee, Krishnendu and De Raaij, Jakob}, booktitle = {The 41st Conference on Uncertainty in Artificial Intelligence}, issn = {2640-3498}, location = {Rio de Janeiro, Brazil}, pages = {223--232}, publisher = {ML Research Press}, title = {{Lower bound on Howard policy iteration for deterministic Markov Decision Processes}}, volume = {286}, year = {2025}, } @inproceedings{20297, abstract = {A standard model that arises in several applications in sequential decision-making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in POMDPs is the reachability objective, where given a target set of states, the goal is to eventually arrive at one of them. The limit-sure problem asks whether reachability can be ensured with probability arbitrarily close to 1. In general, the limit-sure reachability problem for POMDPs is undecidable. However, in many practical cases, the most relevant question is the existence of policies with a small amount of memory. In this work, we study the limit-sure reachability problem for POMDPs with a fixed amount of memory. We establish that the computational complexity of the problem is NP-complete.}, author = {Asadi, Ali and Chatterjee, Krishnendu and Saona Urmeneta, Raimundo J and Shafiee, Ali}, booktitle = {The 41st Conference on Uncertainty in Artificial Intelligence}, issn = {2640-3498}, location = {Rio de Janeiro, Brazil}, pages = {238--247}, publisher = {ML Research Press}, title = {{Limit-sure reachability for small memory policies in POMDPs is NP-complete}}, volume = {286}, year = {2025}, } @article{19508, abstract = {We consider random two-player zero-sum dynamic games with perfect information on a class of infinite directed graphs. Starting from a fixed vertex, the players take turns to move a token along the edges of the graph. Every vertex is assigned a payoff known in advance by both players. Every time the token visits a vertex, Player 2 pays Player 1 the corresponding payoff. We consider a distribution over such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that, when the duration of the game tends to infinity, the value converges almost surely to a constant at an exponential rate dominated in terms of the expansion. On the other hand, for the infinite d-ary tree (that does not fall into the previous class of graphs), we show convergence at a double-exponential rate.}, author = {Attia, Luc and Lichev, Lyuben and Mitsche, Dieter and Saona Urmeneta, Raimundo J and Ziliotto, Bruno}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {1517--1535}, publisher = {Springer Nature}, title = {{Random zero-sum dynamic games on infinite directed graphs}}, doi = {10.1007/s13235-025-00636-4}, volume = {15}, year = {2025}, } @inproceedings{20302, abstract = {LocalSGD and SCAFFOLD are widely used methods in distributed stochastic optimization, with numerous applications in machine learning, large-scale data processing, and federated learning. However, rigorously establishing their theoretical advantages over simpler methods, such as minibatch SGD (MbSGD), has proven challenging, as existing analyses often rely on strong assumptions, unrealistic premises, or overly restrictive scenarios. In this work, we revisit the convergence properties of LocalSGD and SCAFFOLD under a variety of existing or weaker conditions, including gradient similarity, Hessian similarity, weak convexity, and Lipschitz continuity of the Hessian. Our analysis shows that (i) LocalSGD achieves faster convergence compared to MbSGD for weakly convex functions without requiring stronger gradient similarity assumptions; (ii) LocalSGD benefits significantly from higher-order similarity and smoothness; and (iii) SCAFFOLD demonstrates faster convergence than MbSGD for a broader class of non-quadratic functions. These theoretical insights provide a clearer understanding of the conditions under which LocalSGD and SCAFFOLD outperform MbSGD.}, author = {Luo, Ruichen and Stich, Sebastian U. and Horváth, Samuel and Takáč, Martin}, booktitle = {The 28th International Conference on Artificial Intelligence and Statistics}, issn = {2640-3498}, location = {Mai Khao, Thailand}, pages = {2539--2547}, publisher = {ML Research Press}, title = {{Revisiting LocalSGD and SCAFFOLD: Improved rates and missing analysis}}, volume = {258}, year = {2025}, }