Distributed Fractional Bayesian Learning for Adaptive Optimization

This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the optimal solution over a connected network. A general mathematical framework for such a problem has not been studied yet. We aim to provide valuable insights for addressing parameter uncertainty in distributed optimization problems and simultaneously find the optimal solution. Thus, we propose a novel Prediction while Optimization scheme, which utilizes distributed fractional Bayesian learning through weighted averaging on the log-beliefs to update the beliefs of unknown parameters, and distributed gradient descent for renewing the estimation of the optimal solution. Then under suitable assumptions, we prove that all agents' beliefs and decision variables converge almost surely to the true parameter and the optimal solution under the true parameter, respectively. We further establish a sublinear convergence rate for the belief sequence. Finally, numerical experiments are implemented to corroborate the theoretical analysis.

Online Parameter Identification of Generalized Non-cooperative Game

This work studies the parameter identification problem of a generalized non-cooperative game, where each player's cost function is influenced by an observable signal and some unknown parameters. We consider the scenario where equilibrium of the game at some observable signals can be observed with noises, whereas our goal is to identify the unknown parameters with the observed data. Assuming that the observable signals and the corresponding noise-corrupted equilibriums are acquired sequentially, we construct this parameter identification problem as online optimization and introduce a novel online parameter identification algorithm. To be specific, we construct a regularized loss function that balances conservativeness and correctiveness, where the conservativeness term ensures that the new estimates do not deviate significantly from the current estimates, while the correctiveness term is captured by the Karush-Kuhn-Tucker conditions. We then prove that when the players' cost functions are linear with respect to the unknown parameters and the learning rate of the online parameter identification algorithm satisfies \mu_k \propto 1/\sqrt{k}, along with other assumptions, the regret bound of the proposed algorithm is O(\sqrt{K}). Finally, we conduct numerical simulations on a Nash-Cournot problem to demonstrate that the performance of the online identification algorithm is comparable to that of the offline setting.

No-regret learning for repeated non-cooperative games with lossy bandits

This paper considers no-regret learning for repeated continuous-kernel games with lossy bandit feedback. Since it is difficult to give the explicit model of the utility functions in dynamic environments, the players' action can only be learned with bandit feedback. Moreover, because of unreliable communication channels or privacy protection, the bandit feedback may be lost or dropped at random. Therefore, we study the asynchronous online learning strategy of the players to adaptively adjust the next actions for minimizing the long-term regret loss. The paper provides a novel no-regret learning algorithm, called Online Gradient Descent with lossy bandits (OGD-lb). We first give the regret analysis for concave games with differentiable and Lipschitz utilities. Then we show that the action profile converges to a Nash equilibrium with probability 1 when the game is also strictly monotone. We further provide the mean square convergence rate $\mathcal{O}\left(k^{-2\min\{\beta, 1/6\}}\right)$ when the game is $\beta-$ strongly monotone. In addition, we extend the algorithm to the case when the loss probability of the bandit feedback is unknown, and prove its almost sure convergence to Nash equilibrium for strictly monotone games. Finally, we take the resource management in fog computing as an application example, and carry out numerical experiments to empirically demonstrate the algorithm performance.

Distributed Policy Gradient with Variance Reduction in Multi-Agent Reinforcement Learning

This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning (MARL), where agents over a communication network aim to find the optimal policy to maximize the average of all agents' local returns. Due to the non-concave performance function of policy gradient, the existing distributed stochastic optimization methods for convex problems cannot be directly used for policy gradient in MARL. This paper proposes a distributed policy gradient with variance reduction and gradient tracking to address the high variances of policy gradient, and utilizes importance weight to solve the non-stationary problem in the sampling process. We then provide an upper bound on the mean-squared stationary gap, which depends on the number of iterations, the mini-batch size, the epoch size, the problem parameters, and the network topology. We further establish the sample and communication complexity to obtain an $\epsilon$-approximate stationary point. Numerical experiments on the control problem in MARL are performed to validate the effectiveness of the proposed algorithm.