Active Reinforcement Learning (ARL) is a twist on RL where the agent observes reward information only if it pays a cost. This subtle change makes exploration substantially more challenging. Powerful principles in RL like optimism, Thompson sampling, and random exploration do not help with ARL. We relate ARL in tabular environments to Bayes-Adaptive MDPs. We provide an ARL algorithm using Monte-Carlo Tree Search that is asymptotically Bayes optimal. Experimentally, this algorithm is near-optimal on small Bandit problems and MDPs. On larger MDPs it outperforms a Q-learner augmented with specialised heuristics for ARL. By analysing exploration behaviour in detail, we uncover obstacles to scaling up simulation-based algorithms for ARL.
There is a substantial literature on active learning of rewards provided online by humans . @cite_3 learn a reward function on (not actions) from human feedback and use Bayesian optimization techniques to select which trajectories to have labelled. @cite_1 learn a reward function on state-action pairs and their agent optimizes actions to be informative about this function. These reward-learning techniques are aimed at continuous-state environments and do not straightforwardly transfer to our tabular ARL setting. Our work also differs from dorsa2017active in that we optimize for informativeness about the optimal policy and not the true reward function. As Figure illustrates, if some states are unavoidable then their reward is irrelevant to the optimal policy.
@cite_1 @cite_3
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1: Introduction 2: Stochastic bandits: fundamental results 3: Adversarial bandits: fundamental results 4: Contextual Bandits 5: Linear bandits 6: Nonlinear bandits 7: Variants. Acknowledgements. References Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GP-UCB compares favorably with other heuristical GP optimization approaches.