More Like this

1. Approximate Nash Equilibria of Imitation Games: Algorithms and Complexity

   https://doi.org/10.5555/3398761.3398865  

   Murhekar, Aniket and (January 2020, AAMAS Conference proceedings)

   null (Ed.)

   A two-player finite game is represented by two payoff matrices (A, B), one for each player. Imitation games are a subclass of two-player games in which B is the identity matrix, implying that the second player gets a positive payoff only if she "imitates" the first. Given that the problem of computing a Nash equilibrium (NE) is known to be provably hard, even to approximate, we ask if it is any easier for imitation games. We show that much like the general case, for any c > 0, computing a 1 over n^c -approximate NE of imitation games remains PPAD-hard, where n is the number of moves available to the players. On the other hand, we design a polynomial-time algorithm to find ε-approximate NE for any given constant ε > 0 (PTAS). The former result also rules out the smooth complexity being in P, unless PPAD ⊂ RP. 

   more » « less
2. Team-PSRO for Learning Approximate TMECor in Large Team Games via Cooperative Reinforcement Learning

   McAleer, S; Farina, G; Zhou, G; Wang, M; Yang, Y; Sandholm, T (December 2023, NeurIPS23)

   Recent algorithms have achieved superhuman performance at a number of twoplayer zero-sum games such as poker and go. However, many real-world situations are multi-player games. Zero-sum two-team games, such as bridge and football, involve two teams where each member of the team shares the same reward with every other member of that team, and each team has the negative of the reward of the other team. A popular solution concept in this setting, called TMECor, assumes that teams can jointly correlate their strategies before play, but are not able to communicate during play. This setting is harder than two-player zerosum games because each player on a team has different information and must use their public actions to signal to other members of the team. Prior works either have game-theoretic guarantees but only work in very small games, or are able to scale to large games but do not have game-theoretic guarantees. In this paper we introduce two algorithms: Team-PSRO, an extension of PSRO from twoplayer games to team games, and Team-PSRO Mix-and-Match which improves upon Team PSRO by better using population policies. In Team-PSRO, in every iteration both teams learn a joint best response to the opponent’s meta-strategy via reinforcement learning. As the reinforcement learning joint best response approaches the optimal best response, Team-PSRO is guaranteed to converge to a TMECor. In experiments on Kuhn poker and Liar’s Dice, we show that a tabular version of Team-PSRO converges to TMECor, and a version of Team PSRO using deep cooperative reinforcement learning beats self-play reinforcement learning in the large game of Google Research Football. 

   more » « less
3. Differentially Private Nash Equilibrium Seeking in Quadratic Network Games

   https://doi.org/10.1109/TCNS.2024.3398729  

   Wang, Lei; Ding, Kemi; Leng, Yan; Ren, Xiaoqiang; Shi, Guodong (January 2024, IEEE Transactions on Control of Network Systems)

   In this paper, we develop distributed computation algorithms for Nash equilibriums of linear quadratic network games with proven differential privacy guarantees. In a network game with each player's payoff being a quadratic function, the dependencies of the decisions in the payoff function naturally encode a network structure governing the players' inter-personal influences. Such social influence structure and the individual marginal payoffs of the players indicate economic spillovers and individual preferences, and thus they are subject to privacy concerns. For distributed computing of the Nash equilibrium, the players are interconnected by a public communication graph, over which dynamical states are shared among neighboring nodes. When the players' marginal payoffs are considered to be private knowledge, we propose a distributed randomized gradient descent algorithm, in which each player adds a Laplacian random noise to her marginal payoff in the recursive updates. It is proven that the algorithm can guarantee differential privacy and convergence in expectation to the Nash equilibrium of the network game at each player's state. Moreover, the mean-square error between the players' states and the Nash equilibrium is shown to be bounded by a constant related to the differential privacy level. Next, when both the players' marginal payoffs and the influence graph are private information, we propose two distributed algorithms by randomized communication and randomized projection, respectively, for privacy preservation. The differential privacy and convergence guarantees are also established for such algorithms. 

   more » « less
4. Pontryagin neural operator for solving general-sum differential games with parametric state constraints

   Zhang, Lei; Ghimire, Mukesh; Xu, Zhe; Zhang, Wenlong; Ren, Yi (July 2024, 6th Annual Learning for Dynamics & Control Conference)

   The values of two-player general-sum differential games are viscosity solutions to Hamilton-Jacobi-Isaacs (HJI) equations. Value and policy approximations for such games suffer from the curse of dimensionality (CoD). Alleviating CoD through physics-informed neural networks (PINN) encounters convergence issues when value discontinuity is present due to state constraints. On top of these challenges, it is often necessary to learn generalizable values and policies across a parametric space of games, eg, for game parameter inference when information is incomplete. To address these challenges, we propose in this paper a Pontryagin-mode neural operator that outperforms existing state-of-the-art (SOTA) on safety performance across games with parametric state constraints. Our key contribution is the introduction of a costate loss defined on the discrepancy between forward and backward costate rollouts, which are computationally cheap. We show that the discontinuity of costate dynamics (in the presence of state constraints) effectively enables the learning of discontinuous values, without requiring manually supervised data as suggested by the current SOTA. More importantly, we show that the close relationship between costates and policies makes the former critical in learning feedback control policies with generalizable safety performance. 

   more » « less
5. Bayesian Multiagent Inverse Reinforcement Learning for Policy Recommendation

   Martin, C.; Sandholm, T. (January 2021, AAAI-21 Workshop on Reinforcement Learning in Games)

   null (Ed.)

   We study the following problem, which to our knowledge has been addressed only partially in the literature and not in full generality. An agent observes two players play a zero-sum game that is known to the players but not the agent. The agent observes the actions and state transitions of their game play, but not rewards. The players may play either op-timally (according to some Nash equilibrium) or according to any other solution concept, such as a quantal response equilibrium. Following these observations, the agent must recommend a policy for one player, say Player 1. The goal is to recommend a policy that is minimally exploitable un-der the true, but unknown, game. We take a Bayesian ap-proach. We establish a likelihood function based on obser-vations and the specified solution concept. We then propose an approach based on Markov chain Monte Carlo (MCMC), which allows us to approximately sample games from the agent’s posterior belief distribution. Once we have a batch of independent samples from the posterior, we use linear pro-gramming and backward induction to compute a policy for Player 1 that minimizes the sum of exploitabilities over these games. This approximates the policy that minimizes the ex-pected exploitability under the full distribution. Our approach is also capable of handling counterfactuals, where known modifications are applied to the unknown game. We show that our Bayesian MCMC-based technique outperforms two other techniques—one based on the equilibrium policy of the maximum-probability game and the other based on imitation of observed behavior—on all the tested stochastic game envi-ronments. 

   more » « less