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Solving Hamilton-Jacobi-Isaacs (HJI) PDEs numerically enables equilibrial feedback control in two-player differential games, yet faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) have shown promise in…
Finding Nash equilibrial policies for two-player differential games requires solving Hamilton-Jacobi-Isaacs (HJI) PDEs. Self-supervised learning has been used to approximate solutions of such PDEs while circumventing the curse of…
We consider the problem of learning Nash equilibrial policies for two-player risk-sensitive collision-avoiding interactions. Solving the Hamilton-Jacobi-Isaacs equations of such general-sum differential games in real time is an open…
We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic…
This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over time. In the zero-sum game setting, player A minimizes the…
General-sum differential games can approximate values solved by Hamilton-Jacobi-Isaacs (HJI) equations for efficient inference when information is incomplete. However, solving such games through conventional methods encounters the curse of…
Hamilton-Jacobi (HJ) partial differential equations (PDEs) have diverse applications spanning physics, optimal control, game theory, and imaging sciences. This research introduces a first-order optimization-based technique for HJ PDEs,…
This paper introduces a class of continuous-time, finite-player stochastic general-sum differential games that admit solutions through an exact linear PDE system. We formulate a distribution planning game utilizing the cross-log-likelihood…
The values of two-player general-sum differential games are viscosity solutions to Hamilton-Jacobi-Isaacs (HJI) equations. Value and policy approximations for such games suffer from the curse of dimensionality (CoD). Alleviating CoD through…
Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural…
This paper develops a hierarchical games-in-games control architecture for hybrid stochastic systems governed by regime-switching jump-diffusions. We model the interplay between continuous state dynamics and discrete mode transitions as a…
We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost functionals. Our approach ensures that all system…
In this paper we deal with the problem of existence of a smooth solution of the Hamilton-Jacobi-Bellman-Isaacs (HJBI for short) system of equations associated with nonzero-sum stochastic differential games. We consider the problem in…
Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an $H_\infty$ control problem. The solution to these problems can be obtained by solving the…
In the context of multi-player, general-sum games, there is an increasing interest in solution concepts modeling some form of communication among players, since they can lead to socially better outcomes with respect to Nash equilibria, and…
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…
Multi-agent games are becoming an increasing prevalent formalism for the study of electronic commerce and auctions. The speed at which transactions can take place and the growing complexity of electronic marketplaces makes the study of…
Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are…
Hamilton-Jacobi partial differential equations (HJ PDEs) play a central role in many applications such as economics, physics, and engineering. These equations describe the evolution of a value function which encodes valuable information…
We propose a novel numerical method for high dimensional Hamilton--Jacobi--Bellman (HJB) type elliptic partial differential equations (PDEs). The HJB PDEs, reformulated as optimal control problems, are tackled by the actor-critic framework…