Consider a team of cooperative players that take actions in a networkedenvironment. At each turn, each player chooses an action and receives a reward that is an unknown function of all the players' actions. The goal of the team of players is to learn to play together the action profile that maximizes the sum of their rewards. However, players cannot observe the actions or rewards of other players, and can only get this information by communicating with their neighbors.

This search does not affect the computational complexity, which is O(νnDE +SE) for agent n that computes DE parallel consensus steps and goes over a listofSE actionprofiles. Intuitively,wewouldneedE KN tofindtheoptimalactionprofile even with no noise, which creates delays where agents have to wait for their average reward to go abovetheirλn. In the multitasking robots game, if agent n has Ren = 0, then theoptimalactionprofilea e hastosatisfya e,m = nforallm. Ifλisasafemarginawayfromthe boundary of C(G), then most agents will have Ren = 0 most of the time. Hence, their performance depends on the best action profile in SE.

Our main observation is that the gap between λnt and the accumulated reward of agent n, which we call the QoS regret, behaves like a queue.

Consider a team of cooperative players that take actions in a networked-environment. At each turn, each player chooses an action and receives a reward that is an unknown function of all the players' actions. The goal of the team of players is to learn to play together the action profile that maximizes the sum of their rewards. However, players cannot observe the actions or rewards of other players, and can only get this information by communicating with their neighbors. We design a distributed learning algorithm that overcomes the informational bias players have towards maximizing the rewards of nearby players they got more information about. We assume twice continuously differentiable reward functions and constrained convex and compact action sets. Our communication graph is a random time-varying graph that follows an ergodic Markov chain. We prove that even if at every turn players take actions based only on the small random subset of the players' rewards that they know, our algorithm converges with probability 1 to the set of stationary points of (projected) gradient ascent on the sum of rewards function. Hence, if the sum of rewards is concave, then the algorithm converges with probability 1 to the optimal action profile.

Radio resource management in modern cellular networks often calls for the optimization of complex utility functions that are potentially conflicting between different base stations (BSs). Coordinating the resource allocation strategies efficiently across BSs to ensure stable network service poses significant challenges, especially when each utility is accessible only via costly, black-box evaluations. This paper considers formulating the resource allocation among spectrum sharing BSs as a non-cooperative game, with the goal of aligning their allocation incentives toward a stable outcome. To address this challenge, we propose PPR-UCB, a novel Bayesian optimization (BO) strategy that learns from sequential decision-evaluation pairs to approximate pure Nash equilibrium (PNE) solutions. PPR-UCB applies martingale techniques to Gaussian process (GP) surrogates and constructs high probability confidence bounds for utilities uncertainty quantification. Experiments on downlink transmission power allocation in a multi-cell multi-antenna system demonstrate the efficiency of PPR-UCB in identifying effective equilibrium solutions within a few data samples.

Reinforcement-based learning has attracted considerable attention both in modeling human behavior as well as in engineering, for designing measurement- or payoff-based optimization schemes. Such learning schemes exhibit several advantages, especially in relation to filtering out noisy observations. However, they may exhibit several limitations when applied in a distributed setup. In multi-player weakly-acyclic games, and when each player applies an independent copy of the learning dynamics, convergence to (usually desirable) pure Nash equilibria cannot be guaranteed. Prior work has only focused on a small class of games, namely potential and coordination games. To address this main limitation, this paper introduces a novel payoff-based learning scheme for distributed optimization, namely aspiration-based perturbed learning automata (APLA). In this class of dynamics, and contrary to standard reinforcement-based learning schemes, each player's probability distribution for selecting actions is reinforced both by repeated selection and an aspiration factor that captures the player's satisfaction level. We provide a stochastic stability analysis of APLA in multi-player positive-utility games under the presence of noisy observations. This is the first part of the paper that characterizes stochastic stability in generic non-zero-sum games by establishing equivalence of the induced infinite-dimensional Markov chain with a finite dimensional one. In the second part, stochastic stability is further specialized to weakly acyclic games.

Controlling payoffs in repeated games is one of the important topics in control theory of multi-agent systems. Recently proposed zero-determinant strategies enable players to unilaterally enforce linear relations between payoffs. Furthermore, based on the mathematics of zero-determinant strategies, regional payoff control, in which payoffs are enforced into some feasible regions, has been discovered in social dilemma situations. More recently, theory of payoff control was extended to multichannel games, where players parallelly interact with each other in multiple channels. However, the existence of payoff-controlling strategies in multichannel games seems to require the existence of payoff-controlling strategies in some channels, and properties of zero-determinant strategies specific to multichannel games are still not clear. In this paper, we elucidate properties of zero-determinant strategies in multichannel games. First, we relate the existence condition of zero-determinant strategies in multichannel games to that of zero-determinant strategies in each channel. We then show that the existence of zero-determinant strategies in multichannel games requires the existence of zero-determinant strategies in some channels. This result implies that the existence of zero-determinant strategies in multichannel games is tightly restricted by structure of games played in each channel.

In ethics, individual responsibility is often defined through Frankfurt's principle of alternative possibilities. This definition is not adequate in a group decision-making setting because it often results in the lack of a responsible party or "responsibility gap''. One of the existing approaches to address this problem is to consider group responsibility. Another, recently proposed, approach is "higher-order'' responsibility. The paper considers the problem of deciding if higher-order responsibility up to degree $d$ is enough to close the responsibility gap. The main technical result is that this problem is $Π_{2d+1}$-complete.