相关论文: The Gambler's Problem and Beyond

Blackjack or "21" is a popular card-based game of chance and skill. The objective of the game is to win by obtaining a hand total higher than the dealer's without exceeding 21. The ideal blackjack strategy will maximize financial return in…

In reinforcement learning, the goal is to seek rewards and avoid punishments. A simple scalar captures the value of a state or of taking an action, where expected future rewards increase and punishments decrease this quantity. Naturally an…

We study a class of zero-sum stochastic games between a stopper and a singular-controller, previously considered in [Bovo and De Angelis (2025)]. The underlying singularly-controlled dynamics takes values in…

We explore the behaviour emerging from learning agents repeatedly interacting strategically for a wide range of learning dynamics, including $Q$-learning, projected gradient, replicator and log-barrier dynamics. Going beyond the better…

Fictitious play with reinforcement learning is a general and effective framework for zero-sum games. However, using the current deep neural network models, the implementation of fictitious play faces crucial challenges. Neural network model…

Inverse reinforcement learning (IRL) is the problem of finding a reward function that generates a given optimal policy for a given Markov Decision Process. This paper looks at an algorithmic-independent geometric analysis of the IRL problem…

We consider the problem of learning to exploit learning algorithms through repeated interactions in games. Specifically, we focus on the case of repeated two player, finite-action games, in which an optimizer aims to steer a no-regret…

This paper investigates value function approximation in the context of zero-sum Markov games, which can be viewed as a generalization of the Markov decision process (MDP) framework to the two-agent case. We generalize error bounds from MDPs…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

We address the problem of reinforcement learning in which observations may exhibit an arbitrary form of stochastic dependence on past observations and actions. The task for an agent is to attain the best possible asymptotic reward where the…

The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of…

Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…

Reinforcement Learning agents are expected to eventually perform well. Typically, this takes the form of a guarantee about the asymptotic behavior of an algorithm given some assumptions about the environment. We present an algorithm for a…

Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on…

Reinforcement learning has been explored for many problems, from video games with deterministic environments to portfolio and operations management in which scenarios are stochastic; however, there have been few attempts to test these…

Inverse Reinforcement Learning addresses the problem of inferring an expert's reward function from demonstrations. However, in many applications, we not only have access to the expert's near-optimal behavior, but we also observe part of her…

Safety is a primary concern when applying reinforcement learning to real-world control tasks, especially in the presence of external disturbances. However, existing safe reinforcement learning algorithms rarely account for external…

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and…

Motivated by the recent success of reinforcement learning in games such as Go and Dota2, we formulate Bell non-local games as a reinforcement learning problem. Such a formulation helps us to explore Bell non-locality in a range of…

Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important…