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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…

Reinforcement learning algorithms based on Q-learning are driving Deep Reinforcement Learning (DRL) research towards solving complex problems and achieving super-human performance on many of them. Nevertheless, Q-Learning is known to be…

We study how the learning rate affects the performance of a relaxed randomized Kaczmarz algorithm for solving $A x \approx b + \varepsilon$, where $A x =b$ is a consistent linear system and $\varepsilon$ has independent mean zero random…

In stochastic Nash equilibrium problems (SNEPs), it is natural for players to be uncertain about their complex environments and have multi-dimensional unknown parameters in their models. Among various SNEPs, this paper focuses on locally…

In goal-reaching reinforcement learning (RL), the optimal value function has a particular geometry, called quasimetric structure. This paper introduces Quasimetric Reinforcement Learning (QRL), a new RL method that utilizes quasimetric…

Natural Evolution Strategies (NES) is a promising framework for black-box continuous optimization problems. NES optimizes the parameters of a probability distribution based on the estimated natural gradient, and one of the key parameters…

Q-shaping is an extension of Q-value initialization and serves as an alternative to reward shaping for incorporating domain knowledge to accelerate agent training, thereby improving sample efficiency by directly shaping Q-values. This…

Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning…

In many real-world scenarios involving high-stakes and safety implications, a human decision-maker (HDM) may receive recommendations from an artificial intelligence while holding the ultimate responsibility of making decisions. In this…

Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…

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…

Stochastic control with both inherent random system noise and lack of knowledge on system parameters constitutes the core and fundamental topic in reinforcement learning (RL), especially under non-episodic situations where online learning…

Reinforcement learning (RL) has seen significant research and application results but often requires large amounts of training data. This paper proposes two data-efficient off-policy RL methods that use parametrized Q-learning. In these…

This paper investigates posterior sampling algorithms for competitive reinforcement learning (RL) in the context of general function approximations. Focusing on zero-sum Markov games (MGs) under two critical settings, namely self-play and…

An agent's ability to leverage past experience is critical for efficiently solving new tasks. Prior work has focused on using value function estimates to obtain zero-shot approximations for solutions to a new task. In soft Q-learning, we…

Two issues of algorithmic collusion are addressed in this paper. First, we show that in a general class of symmetric games, including Prisoner's Dilemma, Bertrand competition, and any (nonlinear) mixture of first and second price auction,…

We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…

The endeavor of artificial intelligence (AI) is to design autonomous agents capable of achieving complex tasks. Namely, reinforcement learning (RL) proposes a theoretical background to learn optimal behaviors. In practice, RL algorithms…

This paper addresses the problem of distributed online generalized Nash equilibrium (GNE) learning for multi-cluster games with delayed feedback information. Specifically, each agent in the game is assumed to be informed a sequence of local…

We initiate the study of Preference-Based Multi-Agent Reinforcement Learning (PbMARL), exploring both theoretical foundations and empirical validations. We define the task as identifying the Nash equilibrium from a preference-only offline…