HRL lead to improved sample complexity, and how much of an improvement can it provide? Theoretical work on sample-complexity bound in Machine Learning has been integral to the development of the field.

We study Gaussian Process Thompson Sampling (GP-TS) for sequential decision-making over compact, continuous action spaces and provide a frequentist regret analysis based on fractional Gaussian process posteriors, without relying on domain discretization as in prior work. We show that the variance inflation commonly assumed in existing analyses of GP-TS can be interpreted as Thompson Sampling with respect to a fractional posterior with tempering parameter $α\in (0,1)$. We derive a kernel-agnostic regret bound expressed in terms of the information gain parameter $γ_t$ and the posterior contraction rate $ε_t$, and identify conditions on the Gaussian process prior under which $ε_t$ can be controlled. As special cases of our general bound, we recover regret of order $\tilde{\mathcal{O}}(T^{\frac{1}{2}})$ for the squared exponential kernel, $\tilde{\mathcal{O}}(T^{\frac{2ν+3d}{2(2ν+d)}} )$ for the Matérn-$ν$ kernel, and a bound of order $\tilde{\mathcal{O}}(T^{\frac{2ν+3d}{2(2ν+d)}})$ for the rational quadratic kernel. Overall, our analysis provides a unified and discretization-free regret framework for GP-TS that applies broadly across kernel classes.

RL is essentially distinct from and probably harder than that in standard offline RL.

However, existing offline RL methods tend to behave poorly during fine-tuning. In this paper, we study the fine-tuning problem in the context of conservative offline RL methods and we devise an approach for learning an effective initialization from offline data that also enables fast online fine-tuning capabilities.

Deep reinforcement learning (RL) is notoriously impractical to deploy due to sample inefficiency.

This phenomenon cannot be easily explained by offline RL's return maximization objective.