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In this paper, we investigate the power of {\it regularization}, a common technique in reinforcement learning and optimization, in solving extensive-form games (EFGs). We propose a series of new algorithms based on regularizing the payoff…
We study the application of iterative first-order methods to the problem of computing equilibria of large-scale two-player extensive-form games. First-order methods must typically be instantiated with a regularizer that serves as a…
Self-play methods based on regret minimization have become the state of the art for computing Nash equilibria in large two-players zero-sum extensive-form games. These methods fundamentally rely on the hierarchical structure of the players'…
We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…
We study the performance of optimistic regret-minimization algorithms for both minimizing regret in, and computing Nash equilibria of, zero-sum extensive-form games. In order to apply these algorithms to extensive-form games, a…
There has been tremendous recent progress on equilibrium-finding algorithms for zero-sum imperfect-information extensive-form games, but there has been a puzzling gap between theory and practice. First-order methods have significantly…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium.…
The extensive-form game has been studied considerably in recent years. It can represent games with multiple decision points and incomplete information, and hence it is helpful in formulating games with uncertain inputs, such as poker. We…
We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient…
We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…
A conceptually appealing approach for learning Extensive-Form Games (EFGs) is to convert them to Normal-Form Games (NFGs). This approach enables us to directly translate state-of-the-art techniques and analyses in NFGs to learning EFGs, but…
We propose new restarting strategies for the accelerated coordinate descent method. Our main contribution is to show that for a well chosen sequence of restarting times, the restarted method has a nearly geometric rate of convergence. A…
Coordinate descent algorithms are popular for huge-scale optimization problems due to their low cost per-iteration. Coordinate descent methods apply to problems where the constraint set is separable across coordinates. In this paper, we…
Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$…
Regret-based algorithms are highly efficient at finding approximate Nash equilibria in sequential games such as poker games. However, most regret-based algorithms, including counterfactual regret minimization (CFR) and its variants, rely on…
Extensive-form games (EFGs) provide a powerful framework for modeling sequential decision making, capturing strategic interaction under imperfect information, chance events, and temporal structure. Most positive algorithmic and theoretical…
The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient…
Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…