In Reinforcement Learning, it is common to use optimistic initialization of value functions to encourage exploration. However, such an approach generally depends on the domain, viz., the scale of the rewards must be known, and, when using function approximation, the feature representation must have a constant norm. We present a simple approach that performs optimistic initialization with less dependence on the domain.

This paper presents a divide-and-conquer decomposition for solving continuous state reinforcement learning problems. The contribution lies in a method for stitching together continuous state subtasks in a near-seamless manner along wide continuous boundaries. We introduce the concept of Termination Approximation where the set of subtask termination states are covered by goal sets to generate a set of subtask option policies. The approach employs hierarchical reinforcement learning methods and exploits any underlying repetition in continuous problems to allow reuse of the option policies both within a problem and across related problems. The approach is illustrated using a series of challenging racecar problems.

In reinforcement learning, the goal is to seek rewards and avoid punishments. A simple scalar captures the value of a state or of taking an action, where expected future rewards increase and punishments decrease this quantity. Naturally an agent should learn to predict this quantity to take beneficial actions, and many value function approximators exist for this purpose. In the present work, however, we show how value function approximators can cause confusion between predictors of an outcome of one valence (e.g., a signal of reward) and the inhibitor of the opposite valence (e.g., a signal canceling expectation of punishment). We show this to be a problem for both linear and non-linear value function approximators, especially when the amount of data (or experience) is limited. We propose and evaluate a simple resolution: to instead predict reward and punishment values separately, and rectify and add them to get the value needed for decision making. We evaluate several function approximators in this slightly different value function approximation architecture and show that this approach is able to circumvent the confusion and thereby achieve lower value-prediction errors.

Shannon's information entropy measures of the uncertainty of an event's outcome. If learning about a system reflects a decrease in uncertainty, then a plausible intuition is that learning should be accompanied by a decrease in the entropy of the organism's actions and/or perceptual states. To address whether this intuition is valid, I examined an artificial organism -- a simple robot -- that learned to navigate in an arena and analyzed the entropy of the outcome variables action, state, and reward. Entropy did indeed decrease in the initial stages of learning, but two factors complicated the scenario: (1) the introduction of new options discovered during the learning process and (2) the shifting patterns of perceptual and environmental states resulting from changes to the robot's learned movement strategies. These factors lead to a subsequent increase in entropy as the agent learned. I end with a discussion of the utility of information-based characterizations of learning.

In clinical practice, physicians make a series of treatment decisions over the course of a patient's disease based on his/her baseline and evolving characteristics. A dynamic treatment regime is a set of sequential decision rules that operationalizes this process. Each rule corresponds to a decision point and dictates the next treatment action based on the accrued information. Using existing data, a key goal is estimating the optimal regime, that, if followed by the patient population, would yield the most favorable outcome on average. Q- and A-learning are two main approaches for this purpose. We provide a detailed account of these methods, study their performance, and illustrate them using data from a depression study.

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This paper presents a way of solving Markov Decision Processes that combines state abstraction and temporal abstraction. Specifically, we combine state aggregation with the options framework and demonstrate that they work well together and indeed it is only after one combines the two that the full benefit of each is realized. We introduce a hierarchical value iteration algorithm where we first coarsely solve subgoals and then use these approximate solutions to exactly solve the MDP. This algorithm solved several problems faster than vanilla value iteration.

In Reinforcement Learning (RL), state-of-the-art algorithms require a large number of samples per state-action pair to estimate the transition kernel $p$. In many problems, a good approximation of $p$ is not needed. For instance, if from one state-action pair $(s,a)$, one can only transit to states with the same value, learning $p(\cdot|s,a)$ accurately is irrelevant (only its support matters). This paper aims at capturing such behavior by defining a novel hardness measure for Markov Decision Processes (MDPs) we call the {\em distribution-norm}. The distribution-norm w.r.t.~a measure $\nu$ is defined on zero $\nu$-mean functions $f$ by the standard variation of $f$ with respect to $\nu$. We first provide a concentration inequality for the dual of the distribution-norm. This allows us to replace the generic but loose $||\cdot||_1$ concentration inequalities used in most previous analysis of RL algorithms, to benefit from this new hardness measure. We then show that several common RL benchmarks have low hardness when measured using the new norm. The distribution-norm captures finer properties than the number of states or the diameter and can be used to assess the difficulty of MDPs.

Bayes-adaptive planning offers a principled solution to the explorationexploitation trade-offunder model uncertainty. It finds the optimal policy in belief space, which explicitly accounts for the expected effect on future rewards of reductions in uncertainty. However, the Bayes-adaptive solution is typically intractable indomains with large or continuous state spaces. We present a tractable method for approximating the Bayes-adaptive solution by combining simulationbased searchwith a novel value function approximation technique that generalises appropriately over belief space. Our method outperforms prior approaches in both discrete bandit tasks and simple continuous navigation and control tasks.

Any reinforcement learning algorithm that applies to all Markov decision processes (MDPs) will suffer $\Omega(\sqrt{SAT})$ regret on some MDP, where $T$ is the elapsed time and $S$ and $A$ are the cardinalities of the state and action spaces. This implies $T = \Omega(SA)$ time to guarantee a near-optimal policy. In many settings of practical interest, due to the curse of dimensionality, $S$ and $A$ can be so enormous that this learning time is unacceptable. We establish that, if the system is known to be a \emph{factored} MDP, it is possible to achieve regret that scales polynomially in the number of \emph{parameters} encoding the factored MDP, which may be exponentially smaller than $S$ or $A$. We provide two algorithms that satisfy near-optimal regret bounds in this context: posterior sampling reinforcement learning (PSRL) and an upper confidence bound algorithm (UCRL-Factored).