Multiple-policy Evaluation via Density Estimation

• URL: http://arxiv.org/abs/2404.00195v2
• Date: Mon, 27 May 2024 23:57:02 GMT
• Title: Multiple-policy Evaluation via Density Estimation
• Authors: Yilei Chen, Aldo Pacchiano, Ioannis Ch. Paschalidis,
• Abstract summary: We propose an algorithm named $mathrmCAESAR$ for this problem. Up to low order and logarithmic terms $mathrmCAESAR$ achieves a sample complexity $tildeOleft(fracH4epsilon2sum_h=1Hmax_kin[K]sum_s,afrac(d_hpik(s,a))2mu*_h(s,a)right)$, where $dpi
• Score: 30.914344538340412
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the multiple-policy evaluation problem where we are given a set of $K$ policies and the goal is to evaluate their performance (expected total reward over a fixed horizon) to an accuracy $\epsilon$ with probability at least $1-\delta$. We propose an algorithm named $\mathrm{CAESAR}$ for this problem. Our approach is based on computing an approximate optimal offline sampling distribution and using the data sampled from it to perform the simultaneous estimation of the policy values. $\mathrm{CAESAR}$ has two phases. In the first we produce coarse estimates of the visitation distributions of the target policies at a low order sample complexity rate that scales with $\tilde{O}(\frac{1}{\epsilon})$. In the second phase, we approximate the optimal offline sampling distribution and compute the importance weighting ratios for all target policies by minimizing a step-wise quadratic loss function inspired by the DualDICE \cite{nachum2019dualdice} objective. Up to low order and logarithmic terms $\mathrm{CAESAR}$ achieves a sample complexity $\tilde{O}\left(\frac{H^4}{\epsilon^2}\sum_{h=1}^H\max_{k\in[K]}\sum_{s,a}\frac{(d_h^{\pi^k}(s,a))^2}{\mu^*_h(s,a)}\right)$, where $d^{\pi}$ is the visitation distribution of policy $\pi$, $\mu^*$ is the optimal sampling distribution, and $H$ is the horizon.

Related papers

• Robust Distribution Learning with Local and Global Adversarial Corruptions [17.22168727622332]
  We develop an efficient finite-sample algorithm with error bounded by $sqrtvarepsilon k + rho + tildeO(dsqrtkn-1/(k lor 2))$ when $P$ has bounded covariance. Our efficient procedure relies on a novel trace norm approximation of an ideal yet intractable 2-Wasserstein projection estimator.
  arXiv  Detail & Related papers  (2024-06-10T17:48:36Z)
• Optimal score estimation via empirical Bayes smoothing [13.685846094715364]
  We study the problem of estimating the score function of an unknown probability distribution $rho*$ from $n$ independent and identically distributed observations in $d$ dimensions. We show that a regularized score estimator based on a Gaussian kernel attains this rate, shown optimal by a matching minimax lower bound.
  arXiv  Detail & Related papers  (2024-02-12T16:17:40Z)
• Estimation and Inference in Distributional Reinforcement Learning [28.253677740976197]
  We show that a dataset of size $widetilde Oleft(frac|mathcalS||mathcalA|epsilon2 (1-gamma)4right)$ suffices to ensure the Kolmogorov metric and total variation metric between $hatetapi$ and $etapi$ is below $epsilon$ with high probability. Our findings give rise to a unified approach to statistical inference of a wide class of statistical functionals of $etapi$.
  arXiv  Detail & Related papers  (2023-09-29T14:14:53Z)
• ReSQueing Parallel and Private Stochastic Convex Optimization [59.53297063174519]
  We introduce a new tool for BFG convex optimization (SCO): a Reweighted Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. We develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings.
  arXiv  Detail & Related papers  (2023-01-01T18:51:29Z)
• Near Sample-Optimal Reduction-based Policy Learning for Average Reward MDP [58.13930707612128]
  This work considers the sample complexity of obtaining an $varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP) We prove an upper bound of $widetilde O(H varepsilon-3 ln frac1delta)$ samples per state-action pair, where $H := sp(h*)$ is the span of bias of any optimal policy, $varepsilon$ is the accuracy and $delta$ is the failure probability.
  arXiv  Detail & Related papers  (2022-12-01T15:57:58Z)
• Best Policy Identification in Linear MDPs [70.57916977441262]
  We investigate the problem of best identification in discounted linear Markov+Delta Decision in the fixed confidence setting under a generative model. The lower bound as the solution of an intricate non- optimization program can be used as the starting point to devise such algorithms.
  arXiv  Detail & Related papers  (2022-08-11T04:12:50Z)
• List-Decodable Sparse Mean Estimation via Difference-of-Pairs Filtering [42.526664955704746]
  We develop a novel, conceptually simpler technique for list-decodable sparse mean estimation. In particular, for distributions with "certifiably bounded" $t-th moments in $k$-sparse directions, our algorithm achieves error of $(1/alpha)O (1/t)$ with sample complexity $m = (klog(n))O(t)/alpha(mnt)$. For the special case of Gaussian inliers, our algorithm achieves the optimal error guarantee of $Theta (sqrtlog
  arXiv  Detail & Related papers  (2022-06-10T17:38:18Z)
• Gap-Dependent Unsupervised Exploration for Reinforcement Learning [40.990467706237396]
  We present an efficient algorithm for task-agnostic reinforcement learning. The algorithm takes only $widetildemathcalO (1/epsilon cdot (H3SA / rho + H4 S2 A) )$ episodes of exploration. We show that, information-theoretically, this bound is nearly tight for $rho Theta (1/(HS))$ and $H>1$.
  arXiv  Detail & Related papers  (2021-08-11T20:42:46Z)
• Improved Sample Complexity for Incremental Autonomous Exploration in MDPs [132.88757893161699]
  We learn the set of $epsilon$-optimal goal-conditioned policies attaining all states that are incrementally reachable within $L$ steps. DisCo is the first algorithm that can return an $epsilon/c_min$-optimal policy for any cost-sensitive shortest-path problem.
  arXiv  Detail & Related papers  (2020-12-29T14:06:09Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.