David Sychrovský

David Sychrovský, Michal Šustr, Elnaz Davoodi et al.

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical games, such as playing poker with different public cards or trading correlated assets on the stock market. As these similar games feature similar equilibra, we investigate a way to accelerate equilibrium finding on such a distribution. We present a novel "learning not to regret" framework, enabling us to meta-learn a regret minimizer tailored to a specific distribution. Our key contribution, Neural Predictive Regret Matching, is uniquely meta-learned to converge rapidly for the chosen distribution of games, while having regret minimization guarantees on any game. We validated our algorithms' faster convergence on a distribution of river poker games. Our experiments show that the meta-learned algorithms outpace their non-meta-learned counterparts, achieving more than tenfold improvements.

David Sychrovský, Sameer Desai, Martin Loebl

In many real world situations, like minor traffic offenses in big cities, a central authority is tasked with periodic administering punishments to a large number of individuals. Common practice is to give each individual a chance to suffer a smaller fine and be guaranteed to avoid the legal process with probable considerably larger punishment. However, thanks to the large number of offenders and a limited capacity of the central authority, the individual risk is typically small and a rational individual will not choose to pay the fine. Here we show that if the central authority processes the offenders in a publicly known order, it properly incentives the offenders to pay the fine. We show analytically and on realistic experiments that our mechanism promotes non-cooperation and incentives individuals to pay. Moreover, the same holds for an arbitrary coalition. We quantify the expected total payment the central authority receives, and show it increases considerably.

Martin Černý, David Sychrovský, Filip Úradník et al.

Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying a set function requires assigning values to an exponentially large number of subsets in general, a task that is often resource-intensive in practice, particularly when the values derive from external sources such as retraining of machine learning models. A~simple omission of certain values introduces ambiguity that becomes even more significant when the incomplete set function has to be further optimized over. Motivated by the well-known result about inapproximability of subadditive functions using deterministic value queries with respect to a multiplicative error, we study a problem of approximating an unknown subadditive (or a subclass of thereof) set function with respect to an additive error -- i. e., we aim to efficiently close the distance between minimal and maximal completions. Our contributions are threefold: (i) a thorough exploration of minimal and maximal completions of different classes of set functions with missing values and an analysis of their resulting distance; (ii) the development of methods to minimize this distance over classes of set functions with a known prior, achieved by disclosing values of additional subsets in both offline and online manner; and (iii) empirical demonstrations of the algorithms' performance in practical scenarios.

Filip Úradník, David Sychrovský, Jakub Černý et al.

Cooperative game theory has diverse applications in contemporary artificial intelligence, including domains like interpretable machine learning, resource allocation, and collaborative decision-making. However, specifying a cooperative game entails assigning values to exponentially many coalitions, and obtaining even a single value can be resource-intensive in practice. Yet simply leaving certain coalition values undisclosed introduces ambiguity regarding individual contributions to the collective grand coalition. This ambiguity often leads to players holding overly optimistic expectations, stemming from either inherent biases or strategic considerations, frequently resulting in collective claims exceeding the actual grand coalition value. In this paper, we present a framework aimed at optimizing the sequence for revealing coalition values, with the overarching goal of efficiently closing the gap between players' expectations and achievable outcomes in cooperative games. Our contributions are threefold: (i) we study the individual players' optimistic completions of games with missing coalition values along with the arising gap, and investigate its analytical characteristics that facilitate more efficient optimization; (ii) we develop methods to minimize this gap over classes of games with a known prior by disclosing values of additional coalitions in both offline and online fashion; and (iii) we empirically demonstrate the algorithms' performance in practical scenarios, together with an investigation into the typical order of revealing coalition values.

David Sychrovský, Martin Schmid, Michal Šustr et al.

Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in isolation. However, in practice, players often encounter a distribution of similar but distinct games. For example, when trading correlated assets on the stock market, or when refining the strategy in subgames of a much larger game. Recently, offline meta-learning was used to accelerate one-sided equilibrium finding on such distributions. We build upon this, extending the framework to the more challenging self-play setting, which is the basis for most state-of-the-art equilibrium approximation algorithms for domains at scale. When selecting the strategy, our method uniquely integrates information across all decision states, promoting global communication as opposed to the traditional local regret decomposition. Empirical evaluation on normal-form games and river poker subgames shows our meta-learned algorithms considerably outperform other state-of-the-art regret minimization algorithms.

David Sychrovský, Christopher Solinas, Revan MacQueen et al.

Nash equilibrium is perhaps the best-known solution concept in game theory. Such a solution assigns a strategy to each player which offers no incentive to unilaterally deviate. While a Nash equilibrium is guaranteed to always exist, the problem of finding one in general-sum games is PPAD-complete, generally considered intractable. Regret minimization is an efficient framework for approximating Nash equilibria in two-player zero-sum games. However, in general-sum games, such algorithms are only guaranteed to converge to a coarse-correlated equilibrium (CCE), a solution concept where players can correlate their strategies. In this work, we use meta-learning to minimize the correlations in strategies produced by a regret minimizer. This encourages the regret minimizer to find strategies that are closer to a Nash equilibrium. The meta-learned regret minimizer is still guaranteed to converge to a CCE, but we give a bound on the distance to Nash equilibrium in terms of our meta-loss. We evaluate our approach in general-sum imperfect information games. Our algorithms provide significantly better approximations of Nash equilibria than state-of-the-art regret minimization techniques.