Divya Grover

Thomas Kleine Buening, Christos Dimitrakakis, Hannes Eriksson et al.

While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior. However, this is not as easy to specify in sequential decision making as in simple statistical estimation problems. This paper studies (sometimes approximate) minimax-Bayes solutions for various reinforcement learning problems to gain insights into the properties of the corresponding priors and policies. We find that while the worst-case prior depends on the setting, the corresponding minimax policies are more robust than those that assume a standard (i.e. uniform) prior.

Divya Grover, Christos Dimitrakakis

Partially Observable Markov Decision Processes (POMDP) is a widely used model to represent the interaction of an environment and an agent, under state uncertainty. Since the agent does not observe the environment state, its uncertainty is typically represented through a probabilistic belief. While the set of possible beliefs is infinite, making exact planning intractable, the belief space's complexity (and hence planning complexity) is characterized by its covering number. Many POMDP solvers uniformly discretize the belief space and give the planning error in terms of the (typically unknown) covering number. We instead propose an adaptive belief discretization scheme, and give its associated planning error. We furthermore characterize the covering number with respect to the POMDP parameters. This allows us to specify the exact memory requirements on the planner, needed to bound the value function error. We then propose a novel, computationally efficient solver using this scheme. We demonstrate that our algorithm is highly competitive with the state of the art in a variety of scenarios.

Hannes Eriksson, Emilio Jorge, Christos Dimitrakakis et al.

Bayesian reinforcement learning (BRL) offers a decision-theoretic solution for reinforcement learning. While "model-based" BRL algorithms have focused either on maintaining a posterior distribution on models or value functions and combining this with approximate dynamic programming or tree search, previous Bayesian "model-free" value function distribution approaches implicitly make strong assumptions or approximations. We describe a novel Bayesian framework, Inferential Induction, for correctly inferring value function distributions from data, which leads to the development of a new class of BRL algorithms. We design an algorithm, Bayesian Backwards Induction, with this framework. We experimentally demonstrate that the proposed algorithm is competitive with respect to the state of the art.

Divya Grover, Debabrota Basu, Christos Dimitrakakis

We address the problem of Bayesian reinforcement learning using efficient model-based online planning. We propose an optimism-free Bayes-adaptive algorithm to induce deeper and sparser exploration with a theoretical bound on its performance relative to the Bayes optimal policy, with a lower computational complexity. The main novelty is the use of a candidate policy generator, to generate long-term options in the planning tree (over beliefs), which allows us to create much sparser and deeper trees. Experimental results on different environments show that in comparison to the state-of-the-art, our algorithm is both computationally more efficient, and obtains significantly higher reward in discrete environments.