Scalable Multiagent Coordination with Distributed Online Open Loop Planning

We propose distributed online open loop planning (DOOLP), a general framework for online multiagent coordination and decision making under uncertainty. DOOLP is based on online heuristic search in the space defined by a generative model of the domain dynamics, which is exploited by agents to simulate and evaluate the consequences of their potential choices. We also propose distributed online Thompson sampling (DOTS) as an effective instantiation of the DOOLP framework. DOTS models sequences of agent choices by concatenating a number of multiarmed bandits for each agent and uses Thompson sampling for dealing with action value uncertainty. The Bayesian approach underlying Thompson sampling allows to effectively model and estimate uncertainty about (a) own action values and (b) other agents' behavior. This approach yields a principled and statistically sound solution to the exploration-exploitation dilemma when exploring large search spaces with limited resources. We implemented DOTS in a smart factory case study with positive empirical results. We observed effective, robust and scalable planning and coordination capabilities even when only searching a fraction of the potential search space

PAC-Bayesian Analysis of the Exploration-Exploitation Trade-off

We develop a coherent framework for integrative simultaneous analysis of the exploration-exploitation and model order selection trade-offs. We improve over our preceding results on the same subject (Seldin et al., 2011) by combining PAC-Bayesian analysis with Bernstein-type inequality for martingales. Such a combination is also of independent interest for studies of multiple simultaneously evolving martingales.Comment: On-line Trading of Exploration and Exploitation 2 - ICML-2011 workshop. http://explo.cs.ucl.ac.uk/workshop

Heterogeneous Stochastic Interactions for Multiple Agents in a Multi-armed Bandit Problem

We define and analyze a multi-agent multi-armed bandit problem in which decision-making agents can observe the choices and rewards of their neighbors. Neighbors are defined by a network graph with heterogeneous and stochastic interconnections. These interactions are determined by the sociability of each agent, which corresponds to the probability that the agent observes its neighbors. We design an algorithm for each agent to maximize its own expected cumulative reward and prove performance bounds that depend on the sociability of the agents and the network structure. We use the bounds to predict the rank ordering of agents according to their performance and verify the accuracy analytically and computationally

PAC-Bayesian Analysis of Martingales and Multiarmed Bandits

We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This lemma provides an alternative tool to Hoeffding-Azuma inequality to bound concentration of martingale values. Our second approach is based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis. We also introduce a way to apply PAC-Bayesian analysis in situation of limited feedback. We combine the new tools to derive PAC-Bayesian generalization and regret bounds for the multiarmed bandit problem. Although our regret bound is not yet as tight as state-of-the-art regret bounds based on other well-established techniques, our results significantly expand the range of potential applications of PAC-Bayesian analysis and introduce a new analysis tool to reinforcement learning and many other fields, where martingales and limited feedback are encountered