Abstract:
In the Bayesian approach to sequential decision making, exact calculation of the (subjective) utility is intractable. This extends to most special cases of interest, such as reinforcement learning problems. While utility bounds are known to exist for this problem, so far none of them were particularly tight. In this paper, we show how to efficiently calculate a lower bound, which corresponds to the utility of a near-optimal memoryless policy for the decision problem, which is generally different from both the Bayes-optimal policy and the policy which is optimal for the expected MDP under the current belief. We then show how these can be applied to obtain robust exploration policies in a Bayesian reinforcement learning setting.

Abstract:
While in general trading off exploration and exploitation in reinforcement learning is hard, under some formulations relatively simple solutions exist. Optimal decision thresholds for the multi-armed bandit problem, one for the infinite horizon discounted reward case and one for the finite horizon undiscounted reward case are derived, which make the link between the reward horizon, uncertainty and the need for exploration explicit. From this result follow two practical approximate algorithms, which are illustrated experimentally.

Abstract:
We introduce a class of learning problems where the agent is presented with a series of tasks. Intuitively, if there is relation among those tasks, then the information gained during execution of one task has value for the execution of another task. Consequently, the agent is intrinsically motivated to explore its environment beyond the degree necessary to solve the current task it has at hand. We develop a decision theoretic setting that generalises standard reinforcement learning tasks and captures this intuition. More precisely, we consider a multi-stage stochastic game between a learning agent and an opponent. We posit that the setting is a good model for the problem of life-long learning in uncertain environments, where while resources must be spent learning about currently important tasks, there is also the need to allocate effort towards learning about aspects of the world which are not relevant at the moment. This is due to the fact that unpredictable future events may lead to a change of priorities for the decision maker. Thus, in some sense, the model "explains" the necessity of curiosity. Apart from introducing the general formalism, the paper provides algorithms. These are evaluated experimentally in some exemplary domains. In addition, performance bounds are proven for some cases of this problem.

Abstract:
This paper introduces a set of algorithms for Monte-Carlo Bayesian reinforcement learning. Firstly, Monte-Carlo estimation of upper bounds on the Bayes-optimal value function is employed to construct an optimistic policy. Secondly, gradient-based algorithms for approximate upper and lower bounds are introduced. Finally, we introduce a new class of gradient algorithms for Bayesian Bellman error minimisation. We theoretically show that the gradient methods are sound. Experimentally, we demonstrate the superiority of the upper bound method in terms of reward obtained. However, we also show that the Bayesian Bellman error method is a close second, despite its significant computational simplicity.

Abstract:
There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves planning in an infinitely large tree. However, it is possible to obtain stochastic lower and upper bounds on the value of each tree node. This enables us to use stochastic branch and bound algorithms to search the tree efficiently. This paper proposes two such algorithms and examines their complexity in this setting.

Abstract:
We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a random walk within the sequence of covers. We demonstrate the approach on problems of conditional density estimation, which, to our knowledge is the first closed-form, non-parametric Bayesian approach to this problem.

Abstract:
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time. This is because the resulting planning task takes the form of a dynamic programming problem on a belief tree with an infinite number of states. The second type employs relatively simple algorithm which are shown to suffer small regret within a distribution-free framework. This paper presents a lower bound and a high probability upper bound on the optimal value function for the nodes in the Bayesian belief tree, which are analogous to similar bounds in POMDPs. The bounds are then used to create more efficient strategies for exploring the tree. The resulting algorithms are compared with the distribution-free algorithm UCB1, as well as a simpler baseline algorithm on multi-armed bandit problems.

Abstract:
We address the question of whether and how boosting and bagging can be used for speech recognition. In order to do this, we compare two different boosting schemes, one at the phoneme level and one at the utterance level, with a phoneme-level bagging scheme. We control for many parameters and other choices, such as the state inference scheme used. In an unbiased experiment, we clearly show that the gain of boosting methods compared to a single hidden Markov model is in all cases only marginal, while bagging significantly outperforms all other methods. We thus conclude that bagging methods, which have so far been overlooked in favour of boosting, should be examined more closely as a potentially useful ensemble learning technique for speech recognition.

Abstract:
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.