We investigate a class of reinforcement learning dynamics where players adjust their strategies based on actions’ cumulative payoffs over time—specifically, by playing mixed that maximize expected payoff minus regularization term. A widely studied example is exponential learning, process induced an entropic term which leads to evolve according the replicator dynamics. However, in contrast functions used define smooth best responses models stochastic fictitious play, this paper need not be...

Telecommunication networks are converging to a massively distributed cloud infrastructure interconnected with software defined networks. In the envisioned architecture, services will be deployed flexibly and quickly as network slices. Our paper addresses major bottleneck in this context, namely challenge of computing best resource provisioning for slices robust efficient manner. With tractability mind, we propose novel optimization framework which allows fine-grained allocation both terms...

Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond. By necessity, most theoretical guarantees revolve around convex-concave (or even linear) problems; however, making inroads towards efficient GAN training depends crucially on moving beyond this classic framework. To make piecemeal progress along these lines, we analyze the behavior of mirror descent (MD) a class...

We analyze the power allocation problem for orthogonal multiple access channels by means of a non-cooperative potential game in which each user distributes his over available to him. When are static, we show that this possesses unique equilibrium; moreover, if network's users follow distributed learning scheme based on replicator dynamics evolutionary theory, then they converge equilibrium exponentially fast. On other hand, fluctuate stochastically time, associated still admits equilibrium,...

This work proposes a distributed power allocation scheme for maximizing energy efficiency in the uplink of orthogonal frequency-division multiple access (OFDMA)-based heterogeneous networks (HetNets). The user equipment (UEs) network are modeled as rational agents that engage non-cooperative game where each UE allocates its available transmit over set assigned subcarriers so to maximize individual utility (defined user's throughput per Watt power) subject minimum-rate constraints. In this...

To this day, the Internet of Things (IoT) continues its explosive growth. Nevertheless, with exceptional evolution traffic demand, existing infrastructures are struggling to resist. In context, Fog computing is shaping future IoT applications. It offers nearby computational, networking and storage resources respond stringent requirements these However, despite several advantages, raises new challenges which slow adoption down. Hence, there a lack practical solutions enable exploitation novel...

Using a large deviations approach we calculate the probability distribution of mutual information MIMO channels in limit antenna numbers. In contrast to previous methods that only focused at close its mean (thus obtaining an asymptotically Gaussian distribution), full distribution, including tails which strongly deviate from behavior near mean. The resulting interpolates seamlessly between approximation for rates $R$ ergodic value and Zheng Tse signal noise ratios $\rho$. This calculation...

Starting from a heuristic learning scheme for strategic N-person games, we derive new class of continuous-time dynamics consisting replicator-like drift adjusted by penalty term that renders the boundary game’s strategy space repelling. These penalty-regulated are equivalent to players keeping an exponentially discounted aggregate their ongoing payoffs and then using smooth best response pick action based on these performance scores. Owing this inherent duality, proposed satisfy variant folk...

We develop a new stochastic algorithm for solving pseudomonotone variational inequalities. Our method builds on Tseng’s forward-backward-forward algorithm, which is known in the deterministic literature to be valuable alternative Korpelevich’s extragradient when inequalities over convex and closed set governed by Lipschitz continuous operators. The main computational advantage of that it relies only single projection step two independent queries oracle. incorporates minibatch sampling...

Motivated by the recent applications of game-theoretical learning to design distributed control systems, we study a class problems that can be formulated as potential games with continuous action sets. We propose an actor-critic reinforcement algorithm adapts mixed strategies over spaces. To analyze algorithm, extend theory finite-dimensional two-timescale stochastic approximation Banach space setting, and prove dynamics process converge equilibrium in case games. These results combine give...

In this paper, we examine the maximization of energy efficiency (EE) in next-generation multiuser MIMO-OFDM networks that vary dynamically over time-e.g., due to user mobility, fluctuations wireless medium, modulations users' load, etc. Contrary static/stationary regime, system may evolve an arbitrary manner, so users must adjust "on fly," without being able predict state advance. To tackle these issues, propose a simple and distributed online optimization policy leads no regret, i.e., it...

Spurred by the enthusiasm surrounding "Big Data" paradigm, mathematical and algorithmic tools of online optimization have found widespread use in problems where trade-off between data exploration exploitation plays a predominant role. This is particular importance to several branches applications signal processing, such as mining, statistical inference, multimedia indexing wireless communications (to name but few). With this mind, aim tutorial paper provide gentle introduction learning...

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand algorithm's convergence properties in non-convex problems. We first show that sequence iterates generated by SGD remains bounded and converges with probability $1$ under a very broad range step-size schedules. Subsequently, going beyond existing positive guarantees, we avoids strict saddle points/manifolds for entire spectrum policies considered. Finally, prove rate Hurwicz minimizers is...

In this paper, we investigate a distributed learning scheme for broad class of stochastic optimization problems and games that arise in signal processing wireless communications. The proposed algorithm relies on the method matrix exponential (MXL) only requires locally computable gradient observations are possibly imperfect and/or obsolete. To analyze it, introduce notion stable Nash equilibrium show is globally convergent to such equilibria - or when an stable. We also derive explicit...

We consider a family of mirror descent strategies for online optimization in continuous-time and we show that they lead to no regret. From more traditional, discrete-time viewpoint, this approach allows us derive the no-regret properties large class algorithms including as special cases exponential weights algorithm, descent, smooth fictitious play vanishingly play. In so doing, obtain unified view many classical regret bounds, can be decomposed into term stemming from considerations which...

In this paper, we present a distributed learning algorithm for the optimization of signal covariance matrices in Gaussian multiple-input and multiple-output (MIMO) multiple access channel with imperfect (and possibly delayed) feedback. The is based on method matrix exponential (MXL) it has same information computation requirements as water-filling. However, unlike water-filling, proposed converges to system's optimum profile even under stochastic uncertainty Moreover, also retains its...

We study repeated games where players use an exponential learning scheme in order to adapt ever-changing environment. If the game's payoffs are subject random perturbations, this leads a new stochastic version of replicator dynamics that is quite different from "aggregate shocks" approach evolutionary game theory. Irrespective perturbations' magnitude, we find strategies which dominated (even iteratively) eventually become extinct and strict Nash equilibria stochastically asymptotically...