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We introduce a contractive abstract dynamic programming framework and related policy iteration algorithms, specifically designed for sequential zero-sum games and minimax problems with a general structure. Aside from greater generality, the…
In this work, we consider the problem of autonomous racing with multiple agents where agents must interact closely and influence each other to compete. We model interactions among agents through a game-theoretical framework and propose an…
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) formally model the problem of planning under world state uncertainty, but POMDPs with continuous actions and…
This work investigates continuous time stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. The control processes are…
This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and…
We consider a non-atomic congestion game where each decision maker performs selfish optimization over states of a common MDP. The decision makers optimize for their own expected costs, and influence each other through congestion effects on…
Reinforcement learning has been successful both empirically and theoretically in single-agent settings, but extending these results to multi-agent reinforcement learning in general-sum Markov games remains challenging. This paper studies…
We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…
We study a subclass of $n$-player stochastic games, namely, stochastic games with independent chains and unknown transition matrices. In this class of games, players control their own internal Markov chains whose transitions do not depend…
We investigate the linear quadratic Gaussian Stackelberg game under a class of nested observation information pattern. Two decision makers implement control strategies relying on different information sets: The follower uses its observation…
Attention control is a key cognitive ability for humans to select information relevant to the current task. This paper develops a computational model of attention and an algorithm for attention-based probabilistic planning in Markov…
We study a stochastic differential game with $N$ competitive players in a linear-quadratic framework with ergodic cost, where $d$-dimensional diffusion processes govern the state dynamics with an unknown common drift (matrix). Assuming a…
This article introduces a class of $Nash$ games among $Stackelberg$ players ($NASPs$), namely, a class of simultaneous non-cooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a…
We study the problem of online learning in two-sided non-stationary matching markets, where the objective is to converge to a stable match. In particular, we consider the setting where one side of the market, the arms, has fixed known set…
In this paper, we consider a sequential stochastic Stackelberg game with two players, a leader and a follower. The follower has access to the state of the system while the leader does not. Assuming that the players act in their respective…
Model-based algorithms -- algorithms that explore the environment through building and utilizing an estimated model -- are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for…
We study a general class of dynamic multi-agent decision problems with asymmetric information and non-strategic agents, which includes dynamic teams as a special case. When agents are non-strategic, an agent's strategy is known to the other…
This paper looks at predictability problems, i.e., wherein an agent must choose its strategy in order to optimize the predictions that an external observer could make. We address these problems while taking into account uncertainties on the…
In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
Designing efficient and rigorous numerical methods for sequential decision-making under uncertainty is a difficult problem that arises in many applications frameworks. In this paper we focus on the numerical solution of a subclass of…