Related papers: Dynamic mean field programming
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…
This paper studies the performative policy learning problem, where agents adjust their features in response to a released policy to improve their potential outcomes, inducing an endogenous distribution shift. There has been growing interest…
We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative…
Motion planning under uncertainty for an autonomous system can be formulated as a Markov Decision Process with a continuous state space. In this paper, we propose a novel solution to this decision-theoretic planning problem that directly…
Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In addition, the intractable element of the infinite…
Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been…
We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite…
We study infinite-horizon Markov Decision Processes (MDPs) with a continuum of heterogeneous agents interacting through a common noise, without assuming exchangeability. We introduce the framework of Conditional Non-Exchangeable Mean Field…
We consider infinite horizon dynamic programming problems, where the control at each stage consists of several distinct decisions, each one made by one of several agents. In an earlier work we introduced a policy iteration algorithm, where…
This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…
In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…
Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for…
We study the policy evaluation problem in multi-agent reinforcement learning, modeled by a Markov decision process. In this problem, the agents operate in a common environment under a fixed control policy, working together to discover the…
We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game…
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to…
Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…