arXiv subjects

Le Cong Dinh

Publications and source records attributed to Le Cong Dinh.

7 recordsLinked to original sources

arXiv2023

Regret-Minimizing Double Oracle for Extensive-Form Games

By incorporating regret minimization, double oracle methods have demonstrated rapid convergence to Nash Equilibrium (NE) in normal-form games and extensive-form games, through algorithms such as online double oracle (ODO) and extensive-form double oracle (XDO), respectively. In this study, we further examine the theoretical convergence rate and sample complexity of such regret minimization-based double oracle methods, utilizing a unified framework called Regret-Minimizing Double Oracle. Based on this framework, we extend ODO to extensive-form games and determine its sample complexity. Moreover, we demonstrate that the sample complexity of XDO can be exponential in the number of information sets $|S|$, owing to the exponentially decaying stopping threshold of restricted games. To solve this problem, we propose the Periodic Double Oracle (PDO) method, which has the lowest sample complexity among regret minimization-based double oracle methods, being only polynomial in $|S|$. Empirical evaluations on multiple poker and board games show that PDO achieves significantly faster convergence than previous double oracle algorithms and reaches a competitive level with state-of-the-art regret minimization methods.

cs.GT↗

arXiv2023

Last Round Convergence and No-Instant Regret in Repeated Games with Asymmetric Information

This paper considers repeated games in which one player has more information about the game than the other players. In particular, we investigate repeated two-player zero-sum games where only the column player knows the payoff matrix A of the game. Suppose that while repeatedly playing this game, the row player chooses her strategy at each round by using a no-regret algorithm to minimize her (pseudo) regret. We develop a no-instant-regret algorithm for the column player to exhibit last round convergence to a minimax equilibrium. We show that our algorithm is efficient against a large set of popular no-regret algorithms of the row player, including the multiplicative weight update algorithm, the online mirror descent method/follow-the-regularized-leader, the linear multiplicative weight update algorithm, and the optimistic multiplicative weight update.

cs.GT↗

arXiv2023

Online Double Oracle

Solving strategic games with huge action space is a critical yet under-explored topic in economics, operations research and artificial intelligence. This paper proposes new learning algorithms for solving two-player zero-sum normal-form games where the number of pure strategies is prohibitively large. Specifically, we combine no-regret analysis from online learning with Double Oracle (DO) methods from game theory. Our method -- \emph{Online Double Oracle (ODO)} -- is provably convergent to a Nash equilibrium (NE). Most importantly, unlike normal DO methods, ODO is \emph{rationale} in the sense that each agent in ODO can exploit strategic adversary with a regret bound of $\mathcal{O}(\sqrt{T k \log(k)})$ where $k$ is not the total number of pure strategies, but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the NE. On tens of different real-world games, ODO outperforms DO, PSRO methods, and no-regret algorithms such as Multiplicative Weight Update by a significant margin, both in terms of convergence rate to a NE and average payoff against strategic adversaries.

cs.AI↗

arXiv2023

Exploiting No-Regret Algorithms in System Design

We investigate a repeated two-player zero-sum game setting where the column player is also a designer of the system, and has full control on the design of the payoff matrix. In addition, the row player uses a no-regret algorithm to efficiently learn how to adapt their strategy to the column player's behaviour over time in order to achieve good total payoff. The goal of the column player is to guide her opponent to pick a mixed strategy which is favourable for the system designer. Therefore, she needs to: (i) design an appropriate payoff matrix $A$ whose unique minimax solution contains the desired mixed strategy of the row player; and (ii) strategically interact with the row player during a sequence of plays in order to guide her opponent to converge to that desired behaviour. To design such a payoff matrix, we propose a novel solution that provably has a unique minimax solution with the desired behaviour. We also investigate a relaxation of this problem where uniqueness is not required, but all the minimax solutions have the same mixed strategy for the row player. Finally, we propose a new game playing algorithm for the system designer and prove that it can guide the row player, who may play a \emph{stable} no-regret algorithm, to converge to a minimax solution.

cs.GT↗

arXiv2023

Achieving Better Regret against Strategic Adversaries

We study online learning problems in which the learner has extra knowledge about the adversary's behaviour, i.e., in game-theoretic settings where opponents typically follow some no-external regret learning algorithms. Under this assumption, we propose two new online learning algorithms, Accurate Follow the Regularized Leader (AFTRL) and Prod-Best Response (Prod-BR), that intensively exploit this extra knowledge while maintaining the no-regret property in the worst-case scenario of having inaccurate extra information. Specifically, AFTRL achieves $O(1)$ external regret or $O(1)$ \emph{forward regret} against no-external regret adversary in comparison with $O(\sqrt{T})$ \emph{dynamic regret} of Prod-BR. To the best of our knowledge, our algorithm is the first to consider forward regret that achieves $O(1)$ regret against strategic adversaries. When playing zero-sum games with Accurate Multiplicative Weights Update (AMWU), a special case of AFTRL, we achieve \emph{last round convergence} to the Nash Equilibrium. We also provide numerical experiments to further support our theoretical results. In particular, we demonstrate that our methods achieve significantly better regret bounds and rate of last round convergence, compared to the state of the art (e.g., Multiplicative Weights Update (MWU) and its optimistic counterpart, OMWU).

cs.LG↗

arXiv2023

Online Markov Decision Processes with Non-oblivious Strategic Adversary

We study a novel setting in Online Markov Decision Processes (OMDPs) where the loss function is chosen by a non-oblivious strategic adversary who follows a no-external regret algorithm. In this setting, we first demonstrate that MDP-Expert, an existing algorithm that works well with oblivious adversaries can still apply and achieve a policy regret bound of $\mathcal{O}(\sqrt{T \log(L)}+τ^2\sqrt{ T \log(|A|)})$ where $L$ is the size of adversary's pure strategy set and $|A|$ denotes the size of agent's action space. Considering real-world games where the support size of a NE is small, we further propose a new algorithm: MDP-Online Oracle Expert (MDP-OOE), that achieves a policy regret bound of $\mathcal{O}(\sqrt{T\log(L)}+τ^2\sqrt{ T k \log(k)})$ where $k$ depends only on the support size of the NE. MDP-OOE leverages the key benefit of Double Oracle in game theory and thus can solve games with prohibitively large action space. Finally, to better understand the learning dynamics of no-regret methods, under the same setting of no-external regret adversary in OMDPs, we introduce an algorithm that achieves last-round convergence result to a NE. To our best knowledge, this is first work leading to the last iteration result in OMDPs.

cs.LG↗

arXiv2022

Playing Coopetitive Polymatrix Games with Small Manipulation Cost

Iterated coopetitive games capture the situation when one must efficiently balance between cooperation and competition with the other agents over time in order to win the game (e.g., to become the player with highest total utility). Achieving this balance is typically very challenging or even impossible when explicit communication is not feasible (e.g., negotiation or bargaining are not allowed). In this paper we investigate how an agent can achieve this balance to win in iterated coopetitive polymatrix games, without explicit communication. In particular, we consider a 3-player repeated game setting in which our agent is allowed to (slightly) manipulate the underlying game matrices of the other agents for which she pays a manipulation cost, while the other agents satisfy weak behavioural assumptions. We first propose a payoff matrix manipulation scheme and sequence of strategies for our agent that provably guarantees that the utility of any opponent would converge to a value we desire. We then use this scheme to design winning policies for our agent. We also prove that these winning policies can be found in polynomial running time. We then turn to demonstrate the efficiency of our framework in several concrete coopetitive polymatrix games, and prove that the manipulation costs needed to win are bounded above by small budgets. For instance, in the social distancing game, a polymatrix version of the lemonade stand coopetitive game, we showcase a policy with an infinitesimally small manipulation cost per round, along with a provable guarantee that, using this policy leads our agent to win in the long-run. Note that our findings can be trivially extended to $n$-player game settings as well (with $n > 3$).

cs.GT↗