Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOnline Sub-Sampling for Reinforcement Learning with General Function Approximation
128
0
0.0
(
0
)
Added by
Dingwen Kong
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Designing provably efficient algorithms with general function approximation is an important open problem in reinforcement learning. Recently, Wang et al.~[2020c] establish a value-based algorithm with general function approximation that enjoys $widetilde{O}(mathrm{poly}(dH)sqrt{K})$footnote{Throughout the paper, we use $widetilde{O}(cdot)$ to suppress logarithm factors. } regret bound, where $d$ depends on the complexity of the function class, $H$ is the planning horizon, and $K$ is the total number of episodes. However, their algorithm requires $Omega(K)$ computation time per round, rendering the algorithm inefficient for practical use. In this paper, by applying online sub-sampling techniques, we develop an algorithm that takes $widetilde{O}(mathrm{poly}(dH))$ computation time per round on average, and enjoys nearly the same regret bound. Furthermore, the algorithm achieves low switching cost, i.e., it changes the policy only $widetilde{O}(mathrm{poly}(dH))$ times during its execution, making it appealing to be implemented in real-life scenarios. Moreover, by using an upper-confidence based exploration-driven reward function, the algorithm provably explores the environment in the reward-free setting. In particular, after $widetilde{O}(mathrm{poly}(dH))/epsilon^2$ rounds of exploration, the algorithm outputs an $epsilon$-optimal policy for any given reward function.
rate research
Read More
Deep reinforcement learning has achieved impressive successes yet often requires a very large amount of interaction data. This result is perhaps unsurprising, as using complicated function approximation often requires more data to fit, and early theoretical results on linear Markov decision processes provide regret bounds that scale with the dimension of the linear approximation. Ideally, we would like to automatically identify the minimal dimension of the approximation that is sufficient to encode an optimal policy. Towards this end, we consider the problem of model selection in RL with function approximation, given a set of candidate RL algorithms with known regret guarantees. The learners goal is to adapt to the complexity of the optimal algorithm without knowing it textit{a priori}. We present a meta-algorithm that successively rejects increasingly complex models using a simple statistical test. Given at least one candidate that satisfies realizability, we prove the meta-algorithm adapts to the optimal complexity with $tilde{O}(L^{5/6} T^{2/3})$ regret compared to the optimal candidates $tilde{O}(sqrt T)$ regret, where $T$ is the number of episodes and $L$ is the number of algorithms. The dimension and horizon dependencies remain optimal with respect to the best candidate, and our meta-algorithmic approach is flexible to incorporate multiple candidate algorithms and models. Finally, we show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds that depend on the gaps between the maximal values attainable by the candidates.
In generative adversarial imitation learning (GAIL), the agent aims to learn a policy from an expert demonstration so that its performance cannot be discriminated from the expert policy on a certain predefined reward set. In this paper, we study GAIL in both online and offline settings with linear function approximation, where both the transition and reward function are linear in the feature maps. Besides the expert demonstration, in the online setting the agent can interact with the environment, while in the offline setting the agent only accesses an additional dataset collected by a prior. For online GAIL, we propose an optimistic generative adversarial policy optimization algorithm (OGAP) and prove that OGAP achieves $widetilde{mathcal{O}}(H^2 d^{3/2}K^{1/2}+KH^{3/2}dN_1^{-1/2})$ regret. Here $N_1$ represents the number of trajectories of the expert demonstration, $d$ is the feature dimension, and $K$ is the number of episodes. For offline GAIL, we propose a pessimistic generative adversarial policy optimization algorithm (PGAP). For an arbitrary additional dataset, we obtain the optimality gap of PGAP, achieving the minimax lower bound in the utilization of the additional dataset. Assuming sufficient coverage on the additional dataset, we show that PGAP achieves $widetilde{mathcal{O}}(H^{2}dK^{-1/2} +H^2d^{3/2}N_2^{-1/2}+H^{3/2}dN_1^{-1/2} )$ optimality gap. Here $N_2$ represents the number of trajectories of the additional dataset with sufficient coverage.
We propose a model-free reinforcement learning algorithm inspired by the popular randomized least squares value iteration (RLSVI) algorithm as well as the optimism principle. Unlike existing upper-confidence-bound (UCB) based approaches, which are often computationally intractable, our algorithm drives exploration by simply perturbing the training data with judiciously chosen i.i.d. scalar noises. To attain optimistic value function estimation without resorting to a UCB-style bonus, we introduce an optimistic reward sampling procedure. When the value functions can be represented by a function class $mathcal{F}$, our algorithm achieves a worst-case regret bound of $widetilde{O}(mathrm{poly}(d_EH)sqrt{T})$ where $T$ is the time elapsed, $H$ is the planning horizon and $d_E$ is the $textit{eluder dimension}$ of $mathcal{F}$. In the linear setting, our algorithm reduces to LSVI-PHE, a variant of RLSVI, that enjoys an $widetilde{mathcal{O}}(sqrt{d^3H^3T})$ regret. We complement the theory with an empirical evaluation across known difficult exploration tasks.
Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)s analysis of the C51 algorithm in terms of the Cramer distance, but their results only apply to the tabular setting and ignore C51s use of a softmax to produce normalized distributions. In this paper we adapt the Cramer distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cramer-based and can be combined to linear function approximation, with formal guarantees in the context of policy evaluation. In allowing the models prediction to be any real vector, we lose the probabilistic interpretation behind the method, but otherwise maintain the appealing properties of distributional approaches. To the best of our knowledge, ours is the first proof of convergence of a distributional algorithm combined with function approximation. Perhaps surprisingly, our results provide evidence that Cramer-based distributional methods may perform worse than directly approximating the value function.
Safety in reinforcement learning has become increasingly important in recent years. Yet, existing solutions either fail to strictly avoid choosing unsafe actions, which may lead to catastrophic results in safety-critical systems, or fail to provide regret guarantees for settings where safety constraints need to be learned. In this paper, we address both problems by first modeling safety as an unknown linear cost function of states and actions, which must always fall below a certain threshold. We then present algorithms, termed SLUCB-QVI and RSLUCB-QVI, for episodic Markov decision processes (MDPs) with linear function approximation. We show that SLUCB-QVI and RSLUCB-QVI, while with emph{no safety violation}, achieve a $tilde{mathcal{O}}left(kappasqrt{d^3H^3T}right)$ regret, nearly matching that of state-of-the-art unsafe algorithms, where $H$ is the duration of each episode, $d$ is the dimension of the feature mapping, $kappa$ is a constant characterizing the safety constraints, and $T$ is the total number of action plays. We further present numerical simulations that corroborate our theoretical findings.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
