Towards Optimal Algorithms For Online Decision Making Under Practical Constraints

Artificial Intelligence is increasingly being used in real-life applications such as driving with autonomous cars; deliveries with autonomous drones; customer support with chat-bots; personal assistant with smart speakers . . . An Artificial Intelligent agent (AI) can be trained to become expert at a task through a system of rewards and punishment, also well known as Reinforcement Learning (RL). However, since the AI will deal with human beings, it also has to follow some moral rules to accomplish any task. For example, the AI should be fair to the other agents and not destroy the environment. Moreover, the AI should not leak the privacy of users’ data it processes. Those rules represent significant challenges in designing AI that we tackle in this thesis through mathematically rigorous solutions.More precisely, we start by considering the basic RL problem modeled as a discrete Markov Decision Process. We propose three simple algorithms (UCRL-V, BUCRL and TSUCRL) using two different paradigms: Frequentist (UCRL-V) and Bayesian (BUCRL and TSUCRL). Through a unified theoretical analysis, we show that our three algorithms are near-optimal. Experiments performed confirm the superiority of our methods compared to existing techniques. Afterwards, we address the issue of fairness in the stateless version of reinforcement learning also known as multi-armed bandit. To concentrate our effort on the key challenges, we focus on two-agents multi-armed bandit. We propose a novel objective that has been shown to be connected to fairness and justice. We derive an algorithm UCRG to solve this novel objective and show theoretically its near-optimality. Next, we tackle the issue of privacy by using the recently introduced notion of Differential Privacy. We design multi-armed bandit algorithms that preserve differential-privacy. Theoretical analyses show that for the same level of privacy, our newly developed algorithms achieve better performance than existing techniques

Mean Field Equilibria for Competitive Exploration in Resource Sharing Settings

We consider a model of nomadic agents exploring and competing for time-varying location-specific resources, arising in crowdsourced transportation services, online communities, and in traditional location based economic activity. This model comprises a group of agents, and a set of locations each endowed with a dynamic stochastic resource process. Each agent derives a periodic reward determined by the overall resource level at her location, and the number of other agents there. Each agent is strategic and free to move between locations, and at each time decides whether to stay at the same node or switch to another one. We study the equilibrium behavior of the agents as a function of dynamics of the stochastic resource process and the nature of the externality each agent imposes on others at the same location. In the asymptotic limit with the number of agents and locations increasing proportionally, we show that an equilibrium exists and has a threshold structure, where each agent decides to switch to a different location based only on their current location's resource level and the number of other agents at that location. This result provides insight into how system structure affects the agents' collective ability to explore their domain to find and effectively utilize resource-rich areas. It also allows assessing the impact of changing the reward structure through penalties or subsidies.Comment: 17 pages, 1 figure, 1 table, to appear in proceedings of the 25th International World Wide Web Conference(WWW2016

On Learning Algorithms for Nash Equilibria

Third International Symposium, SAGT 2010, Athens, Greece, October 18-20, 2010. ProceedingsCan learning algorithms find a Nash equilibrium? This is a natural question for several reasons. Learning algorithms resemble the behavior of players in many naturally arising games, and thus results on the convergence or non-convergence properties of such dynamics may inform our understanding of the applicability of Nash equilibria as a plausible solution concept in some settings. A second reason for asking this question is in the hope of being able to prove an impossibility result, not dependent on complexity assumptions, for computing Nash equilibria via a restricted class of reasonable algorithms. In this work, we begin to answer this question by considering the dynamics of the standard multiplicative weights update learning algorithms (which are known to converge to a Nash equilibrium for zero-sum games). We revisit a 3×3 game defined by Shapley [10] in the 1950s in order to establish that fictitious play does not converge in general games. For this simple game, we show via a potential function argument that in a variety of settings the multiplicative updates algorithm impressively fails to find the unique Nash equilibrium, in that the cumulative distributions of players produced by learning dynamics actually drift away from the equilibrium