Monte Carlo Bayesian Reinforcement Learning

Bayesian reinforcement learning (BRL) encodes prior knowledge of the world in a model and represents uncertainty in model parameters by maintaining a probability distribution over them. This paper presents Monte Carlo BRL (MC-BRL), a simple and general approach to BRL. MC-BRL samples a priori a finite set of hypotheses for the model parameter values and forms a discrete partially observable Markov decision process (POMDP) whose state space is a cross product of the state space for the reinforcement learning task and the sampled model parameter space. The POMDP does not require conjugate distributions for belief representation, as earlier works do, and can be solved relatively easily with point-based approximation algorithms. MC-BRL naturally handles both fully and partially observable worlds. Theoretical and experimental results show that the discrete POMDP approximates the underlying BRL task well with guaranteed performance.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Reinforcement Learning via AIXI Approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.Comment: 8 LaTeX pages, 1 figur

Efficient Bayes-Adaptive Reinforcement Learning using Sample-Based Search

Bayesian model-based reinforcement learning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, finding the resulting Bayes-optimal policies is notoriously taxing, since the search space becomes enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach outperformed prior Bayesian model-based RL algorithms by a significant margin on several well-known benchmark problems -- because it avoids expensive applications of Bayes rule within the search tree by lazily sampling models from the current beliefs. We illustrate the advantages of our approach by showing it working in an infinite state space domain which is qualitatively out of reach of almost all previous work in Bayesian exploration.Comment: 14 pages, 7 figures, includes supplementary material. Advances in Neural Information Processing Systems (NIPS) 201

Bayesian learning of noisy Markov decision processes

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller

Bayesian Policy Gradients via Alpha Divergence Dropout Inference

Policy gradient methods have had great success in solving continuous control tasks, yet the stochastic nature of such problems makes deterministic value estimation difficult. We propose an approach which instead estimates a distribution by fitting the value function with a Bayesian Neural Network. We optimize an $\alpha$-divergence objective with Bayesian dropout approximation to learn and estimate this distribution. We show that using the Monte Carlo posterior mean of the Bayesian value function distribution, rather than a deterministic network, improves stability and performance of policy gradient methods in continuous control MuJoCo simulations.Comment: Accepted to Bayesian Deep Learning Workshop at NIPS 201

Finding Competitive Network Architectures Within a Day Using UCT

The design of neural network architectures for a new data set is a laborious task which requires human deep learning expertise. In order to make deep learning available for a broader audience, automated methods for finding a neural network architecture are vital. Recently proposed methods can already achieve human expert level performances. However, these methods have run times of months or even years of GPU computing time, ignoring hardware constraints as faced by many researchers and companies. We propose the use of Monte Carlo planning in combination with two different UCT (upper confidence bound applied to trees) derivations to search for network architectures. We adapt the UCT algorithm to the needs of network architecture search by proposing two ways of sharing information between different branches of the search tree. In an empirical study we are able to demonstrate that this method is able to find competitive networks for MNIST, SVHN and CIFAR-10 in just a single GPU day. Extending the search time to five GPU days, we are able to outperform human architectures and our competitors which consider the same types of layers

Bayesian Reinforcement Learning via Deep, Sparse Sampling

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.Comment: Published in AISTATS 202

Bayesian multitask inverse reinforcement learning

We generalise the problem of inverse reinforcement learning to multiple tasks, from multiple demonstrations. Each one may represent one expert trying to solve a different task, or as different experts trying to solve the same task. Our main contribution is to formalise the problem as statistical preference elicitation, via a number of structured priors, whose form captures our biases about the relatedness of different tasks or expert policies. In doing so, we introduce a prior on policy optimality, which is more natural to specify. We show that our framework allows us not only to learn to efficiently from multiple experts but to also effectively differentiate between the goals of each. Possible applications include analysing the intrinsic motivations of subjects in behavioural experiments and learning from multiple teachers.Comment: Corrected version. 13 pages, 8 figure