Can Deha Karıksız

Naci Saldi, Can Deha Karıksız, Maxim Raginsky et al.

In this paper, we consider non-signaling approximation of finite stochastic teams. We first introduce a hierarchy of team decision rules that can be classified in an increasing order as randomized policies, quantum-correlated policies, and non-signaling policies. Then, we establish an approximation of team-optimal policies for sequential teams via extendible non-signaling policies. We prove that the distance between extendible non-signaling policies and decentralized policies is small if the extension is sufficiently large. Using this result, we establish a linear programming (LP) approximation of sequential teams. Finally, we state an open problem regarding computation of optimal value of quantum-correlated policies.

Berkay Anahtarci, Can Deha Kariksiz, Naci Saldi

This paper explores the use of Maximum Causal Entropy Inverse Reinforcement Learning (IRL) within the context of discrete-time stationary Mean-Field Games (MFGs) characterized by finite state spaces and an infinite-horizon, discounted-reward setting. Although the resulting optimization problem is non-convex with respect to policies, we reformulate it as a convex optimization problem in terms of state-action occupation measures by leveraging the linear programming framework of Markov Decision Processes. Based on this convex reformulation, we introduce a gradient descent algorithm with a guaranteed convergence rate to efficiently compute the optimal solution. Moreover, we develop a new method that conceptualizes the MFG problem as a Generalized Nash Equilibrium Problem (GNEP), enabling effective computation of the mean-field equilibrium for forward reinforcement learning (RL) problems and marking an advancement in MFG solution techniques. We further illustrate the practical applicability of our GNEP approach by employing this algorithm to generate data for numerical MFG examples.

Berkay Anahtarci, Can Deha Kariksiz, Naci Saldi

We consider the maximum causal entropy inverse reinforcement learning problem for infinite-horizon stationary mean-field games, in which we model the unknown reward function within a reproducing kernel Hilbert space. This allows the inference of rich and potentially nonlinear reward structures directly from expert demonstrations, in contrast to most existing inverse reinforcement learning approaches for mean-field games that typically restrict the reward function to a linear combination of a fixed finite set of basis functions. We also focus on the infinite-horizon cost structure, whereas prior studies primarily rely on finite-horizon formulations. We introduce a Lagrangian relaxation to this maximum causal entropy inverse reinforcement learning problem that enables us to reformulate it as an unconstrained log-likelihood maximization problem, and obtain a solution \lk{via} a gradient ascent algorithm. To illustrate the theoretical consistency of the algorithm, we establish the smoothness of the log-likelihood objective by proving the Fréchet differentiability of the related soft Bellman operators with respect to the parameters in the reproducing kernel Hilbert space. We demonstrate the effectiveness of our method on a mean-field traffic routing game, where it accurately recovers expert behavior.

Berkay Anahtarci, Can Deha Kariksiz, Naci Saldi

In this paper, we introduce a regularized mean-field game and study learning of this game under an infinite-horizon discounted reward function. Regularization is introduced by adding a strongly concave regularization function to the one-stage reward function in the classical mean-field game model. We establish a value iteration based learning algorithm to this regularized mean-field game using fitted Q-learning. The regularization term in general makes reinforcement learning algorithm more robust to the system components. Moreover, it enables us to establish error analysis of the learning algorithm without imposing restrictive convexity assumptions on the system components, which are needed in the absence of a regularization term.

Berkay Anahtarcı, Can Deha Karıksız, Naci Saldi

We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator, whose fixed point is a mean-field equilibrium (i.e. equilibrium in the infinite population limit). We first prove that this operator is a contraction, and propose a learning algorithm to compute an approximate mean-field equilibrium by approximating the MFE operator with a random one. Moreover, using the contraction property of the MFE operator, we establish the error analysis of the proposed learning algorithm. We then show that the learned mean-field equilibrium constitutes an approximate Nash equilibrium for finite-agent games.