Batched bandit problems

Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.Comment: Published at http://dx.doi.org/10.1214/15-AOS1381 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Anterior Prefrontal Cortex Contributes to Action Selection through Tracking of Recent Reward Trends

The functions of prefrontal cortex remain enigmatic, especially for its anterior sectors, putatively ranging from planning to self-initiated behavior, social cognition, task switching, and memory. A predominant current theory regarding the most anterior sector, the frontopolar cortex (FPC), is that it is involved in exploring alternative courses of action, but the detailed causal mechanisms remain unknown. Here we investigated this issue using the lesion method, together with a novel model-based analysis. Eight patients with anterior prefrontal brain lesions including the FPC performed a four-armed bandit task known from neuroimaging studies to activate the FPC. Model-based analyses of learning demonstrated a selective deficit in the ability to extrapolate the most recent trend, despite an intact general ability to learn from past rewards. Whereas both brain-damaged and healthy controls used comparisons between the two most recent choice outcomes to infer trends that influenced their decision about the next choice, the group with anterior prefrontal lesions showed a complete absence of this component and instead based their choice entirely on the cumulative reward history. Given that the FPC is thought to be the most evolutionarily recent expansion of primate prefrontal cortex, we suggest that its function may reflect uniquely human adaptations to select and update models of reward contingency in dynamic environments

Smoothing Policies and Safe Policy Gradients

Policy gradient algorithms are among the best candidates for the much anticipated application of reinforcement learning to real-world control tasks, such as the ones arising in robotics. However, the trial-and-error nature of these methods introduces safety issues whenever the learning phase itself must be performed on a physical system. In this paper, we address a specific safety formulation, where danger is encoded in the reward signal and the learning agent is constrained to never worsen its performance. By studying actor-only policy gradient from a stochastic optimization perspective, we establish improvement guarantees for a wide class of parametric policies, generalizing existing results on Gaussian policies. This, together with novel upper bounds on the variance of policy gradient estimators, allows to identify those meta-parameter schedules that guarantee monotonic improvement with high probability. The two key meta-parameters are the step size of the parameter updates and the batch size of the gradient estimators. By a joint, adaptive selection of these meta-parameters, we obtain a safe policy gradient algorithm