Infomax strategies for an optimal balance between exploration and exploitation

Proper balance between exploitation and exploration is what makes good decisions, which achieve high rewards like payoff or evolutionary fitness. The Infomax principle postulates that maximization of information directs the function of diverse systems, from living systems to artificial neural networks. While specific applications are successful, the validity of information as a proxy for reward remains unclear. Here, we consider the multi-armed bandit decision problem, which features arms (slot-machines) of unknown probabilities of success and a player trying to maximize cumulative payoff by choosing the sequence of arms to play. We show that an Infomax strategy (Info-p) which optimally gathers information on the highest mean reward among the arms saturates known optimal bounds and compares favorably to existing policies. The highest mean reward considered by Info-p is not the quantity actually needed for the choice of the arm to play, yet it allows for optimal tradeoffs between exploration and exploitation.

Belief Propagation and Beyond for Particle Tracking

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid seeded with identical passive particles that diffuse and are advected by a flow. Our approach rests on efficient algorithms to estimate the weighted number of possible matchings among particles in two consecutive snapshots, the partition function of the underlying graphical model. The partition function is then maximized over the model parameters, namely diffusivity and velocity gradient. A Belief Propagation (BP) scheme is the backbone of our algorithm, providing accurate results for the flow parameters we want to learn. The BP estimate is additionally improved by incorporating Loop Series (LS) contributions. For the weighted matching problem, LS is compactly expressed as a Cauchy integral, accurately estimated by a saddle point approximation. Numerical experiments show that the quality of our improved BP algorithm is comparable to the one of a fully polynomial randomized approximation scheme, based on the Markov Chain Monte Carlo (MCMC) method, while the BP-based scheme is substantially faster than the MCMC scheme.