241 research outputs found
Online Regret Bounds for Undiscounted Continuous Reinforcement Learning
We derive sublinear regret bounds for undiscounted reinforcement learning in
continuous state space. The proposed algorithm combines state aggregation with
the use of upper confidence bounds for implementing optimism in the face of
uncertainty. Beside the existence of an optimal policy which satisfies the
Poisson equation, the only assumptions made are Holder continuity of rewards
and transition probabilities
Learning to Control in Metric Space with Optimal Regret
We study online reinforcement learning for finite-horizon deterministic
control systems with {\it arbitrary} state and action spaces. Suppose that the
transition dynamics and reward function is unknown, but the state and action
space is endowed with a metric that characterizes the proximity between
different states and actions. We provide a surprisingly simple upper-confidence
reinforcement learning algorithm that uses a function approximation oracle to
estimate optimistic Q functions from experiences. We show that the regret of
the algorithm after episodes is where is a
smoothness parameter, and is the doubling dimension of the state-action
space with respect to the given metric. We also establish a near-matching
regret lower bound. The proposed method can be adapted to work for more
structured transition systems, including the finite-state case and the case
where value functions are linear combinations of features, where the method
also achieve the optimal regret
Prediction with Expert Advice under Discounted Loss
We study prediction with expert advice in the setting where the losses are
accumulated with some discounting---the impact of old losses may gradually
vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm
for Regression to this case, propose a suitable new variant of exponential
weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte
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