Temporal-Difference Learning

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Temporal-difference (TD) learning studies how to estimate future rewards and improve decisions by updating predictions from the difference between a current estimate and a bootstrapped next-step target. Its methods range from tabular and linear TD with eligibility traces to deep Q-learning, distributional critics, and multi-step or off-policy updates, used in prediction, control, and policy evaluation. Current work develops sharper convergence and uncertainty guarantees for single-trajectory, Markovian data while extending TD to long-horizon, multi-agent, and partially observed settings. A central tension is that bootstrapping makes learning data-efficient, but function approximation, off-policy sampling, and moving targets can cause bias or instability; balancing stability, speed, and accurate credit assignment remains open.

Latest papers

82 papers13 papers in the last four weeks, up 86% on the four weeks before. 0.1% of all new papers.

May 6, 2026

Extending Differential Temporal Difference Methods for Episodic Problems

Differential temporal difference (TD) methods are value-based reinforcement learning algorithms that have been proposed for infinite-horizon problems. They rely on reward centering, where each reward is centered by the average reward. This keeps the return bounded and removes a value function's state-independent offset. However, reward centering can alter the optimal policy in episodic problems, limiting its applicability. Motivated by recent works that emphasize the role of normalization in streaming deep reinforcement learning, we study reward centering in episodic problems and propose a generalization of differential TD. We prove that this generalization maintains the ordering of policies in the presence of termination, and thus extends differential TD to episodic problems. We show equivalence with a form of linear TD, thereby inheriting theoretical guarantees that have been shown for those algorithms. We then extend several streaming reinforcement learning algorithms to their differential counterparts. Across a range of base algorithms and environments, we empirically validate that reward centering can improve sample efficiency in episodic problems.

Kris De Asis, Mohamed Elsayed, Jiamin He

1Openmind Research Institute · Department of Computing Science, University of Alberta, Canada · 3Alberta Machine Intelligence Institute (Amii)

Reinforcement Learning Temporal-Difference Learning

May 3, 2026

Bridging the Gap Between Average and Discounted TD Learning

The analysis of Temporal Difference (TD) learning in the average-reward setting faces notable theoretical difficulties because the Bellman operator is not contractive with respect to any norm. This complicates standard analyses of stochastic updates that are effective in discounted settings. Although a considerable body of literature addresses these challenges, existing theoretical approaches come with limitations. We introduce a novel algorithm designed explicitly for policy evaluation in the average-reward setting, utilizing sampling from two Markovian trajectories. Our proposed method overcomes previous limitations by guaranteeing convergence to the unique solution of a properly defined projected Bellman equation. Notably, and in contrast to earlier work, our convergence analysis is uniformly applicable to both linear function approximation and tabular settings and does not involve explicit dimension-dependent terms in its convergence bounds. These results align with what is known to hold in the discounted setting. Furthermore, our algorithm achieves improved dependence on the problem's condition number, reducing the sample complexity from quartic, as in prior literature, to quadratic scaling, and thus matching the efficiency seen in the discounted setting.

Haoxing Tian, Zaiwei Chen, Ioannis Ch. Paschalidis +1

Department of Electrical and Computer Engineering Boston University · Edwardson School of Industrial Engineering Purdue University

Reinforcement Learning Average-Reward RL Stochastic Approximation Policy Evaluation Temporal-Difference Learning Linear Function Approximation

May 3, 2026

AdamO: A Collapse-Suppressed Optimizer for Offline RL

Offline reinforcement learning (RL) can fail spectacularly when bootstrapped temporal-difference (TD) updates amplify their own errors, driving the critic toward extreme and unusable Q-values. A key counterintuitive insight of this work is that collapse is not only a property of the backup rule or network architecture: optimizer dynamics themselves can directly trigger or suppress instability. From a control-theoretic viewpoint, we model offline TD learning as a feedback system and analyze Adam-based critic updates. This yields a necessary and sufficient condition for stability of the induced local update dynamics: within the regime we analyze, these dynamics are stable if and only if the spectral radius of the corresponding update operator is strictly below one. Further analysis suggests that standard Adam updates can inadvertently distort the parameter geometry, motivating explicit orthogonality constraints to prevent TD error amplification. To this end, we propose AdamO, an Adam-based optimizer with a decoupled orthogonality correction regulated by a strict task-alignment budget. We prove that this design theoretically guarantees worst-case task safety and preserves Adam's continuous-time dissipative dynamics. Empirically, AdamO is broadly compatible with diverse offline RL baselines, improving stability and returns across a broad suite of benchmarks.

Nan Qiao, Sheng Yue, Shuning Wang +1

1Tsinghua University, China · 2Central South University, China · 3Sun Yat-sen University, China

Reinforcement Learning Orthogonal Optimization RL Stability Temporal-Difference Learning Offline RL Neural Network Stability

May 2, 2026

Regularized Centered Emphatic Temporal Difference Learning

Off-policy temporal-difference (TD) learning with function approximation faces a structural tradeoff among stability, projection geometry, and variance control. Emphatic TD (ETD) improves the off-policy projection geometry through follow-on emphasis, but the follow-on trace can have high variance. We revisit this tradeoff through Bellman-error centering. Although centering naturally removes a common drift term from TD errors, we show that a naive centered emphatic extension introduces an auxiliary coupling that can destroy the positive-definiteness of the ETD key matrix. We propose Regularized Emphatic Temporal-Difference Learning (RETD), which preserves the follow-on trace and regularizes only the auxiliary centering recursion, corresponding to lifting the lower-right block of the coupled key matrix from

1

to

1+c

. We derive the RETD core matrix, prove convergence under a conservative sufficient regularization condition, and evaluate the method on diagnostic linear off-policy prediction tasks. The experiments show that RETD avoids the instability of naive centered emphatic learning, preserves favorable emphatic geometry, and exhibits a robust intermediate regime for the regularization parameter

c

across the diagnostics.

Xingguo Chen, Chaohui Wu, Jinguo Ye +5

Nanjing University of Posts and Telecommunications · Nanjing University · Microsoft +1

Temporal-Difference Learning

Apr 30, 2026

Bayesian policy gradient and actor-critic algorithms

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate the gradient, which tend to have high variance, requiring many samples and resulting in slow convergence. We first propose a Bayesian framework for policy gradient, based on modeling the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient and a measure of the uncertainty in the gradient estimates, namely, the gradient covariance, are provided at little extra cost. Since the proposed framework considers system trajectories as its basic observable unit, it does not require the dynamics within trajectories to be of any particular form, and can be extended to partially observable problems. On the downside, it cannot exploit the Markov property when the system is Markovian. To address this, we supplement our Bayesian policy gradient framework with a new actor-critic learning model in which a Bayesian class of non-parametric critics, based on Gaussian process temporal difference learning, is used. Such critics model the action-value function as a Gaussian process, allowing Bayes rule to be used to compute the posterior distribution over action-value functions, conditioned on the observed data. Appropriate choices of the policy parameterization and of the prior covariance (kernel) between action-values yield closed-form expressions for the posterior of the gradient of the expected return with respect to the policy parameters. We perform detailed experimental comparisons of the proposed Bayesian policy gradient and actor-critic algorithms with classic Monte-Carlo based policy gradient methods, on a number of reinforcement learning problems.

Mohammad Ghavamzadeh, Yaakov Engel, Michal Valko

Adobe Research & Inria · Rafael Advanced Defence System, Israel · Inria Lille — SequeL team, France

Bayesian RL Temporal-Difference Learning Policy Gradient Methods Actor-Critic Methods Policy Learning

Apr 21, 2026

Intentional Updates for Streaming Reinforcement Learning

In gradient-based learning, a step size chosen in parameter units does not produce a predictable per-step change in function output. This often leads to instability in the streaming setting (i.e., batch size=1), where stochasticity is not averaged out and update magnitudes can momentarily become arbitrarily big or small. Instead, we propose intentional updates: first specify the intended outcome of an update and then solve for the step size that approximately achieves it. This strategy has precedent in online supervised linear regression via Normalized Least Mean Squares algorithm, which selects a step size to yield a specified change in the function output proportional to the current error. We extend this principle to streaming deep reinforcement learning by defining appropriate intended outcomes: Intentional TD aims for a fixed fractional reduction of the TD error, and Intentional Policy Gradient aims for a bounded per-step change in the policy, limiting local KL divergence. We propose practical algorithms combining eligibility traces and diagonal scaling. Empirically, these methods yield state-of-the-art streaming performance, frequently performing on par with batch and replay-buffer approaches.

Arsalan Sharifnassab, Mohamed Elsayed, Kris De Asis +2

Openmind Research Institute · Department of Computing Science, University of Alberta.

Reinforcement Learning Temporal-Difference Learning Policy Gradient Methods Policy Learning Streaming Algorithms

Apr 2, 2026

Pseudo-Quantized Actor-Critic Algorithm for Robustness to Noisy Temporal Difference Error

In reinforcement learning (RL), temporal difference (TD) errors are widely adopted for optimizing value and policy functions. However, since the TD error is defined by a bootstrap method, its computation tends to be noisy and destabilize learning. Heuristics to improve the accuracy of TD errors, such as target networks and ensemble models, have been introduced so far. While these are essential approaches for the current deep RL algorithms, they cause side effects like increased computational cost and reduced learning efficiency. Therefore, this paper revisits the TD learning algorithm based on control as inference, deriving a novel algorithm capable of robust learning against noisy TD errors. First, the distribution model of optimality, a binary random variable, is represented by a sigmoid function. Alongside forward and reverse Kullback-Leibler divergences, this new model derives a robust learning rule: when the sigmoid function saturates with a large TD error probably due to noise, the gradient vanishes, implicitly excluding it from learning. Furthermore, the two divergences exhibit distinct gradient-vanishing characteristics. Building on these analyses, the optimality is decomposed into multiple levels to achieve pseudo-quantization of TD errors, aiming for further noise reduction. Additionally, a Jensen-Shannon divergence-based approach is approximately derived to inherit the characteristics of both divergences. These benefits are verified through RL benchmarks, demonstrating stable learning even when heuristics are insufficient or rewards contain noise.

Taisuke Kobayashi

Principles of Informatics Research Division, National Institute of Informatics (NII), 2-1-2 Hitotsubashi, Chiyoda-ku, 101-8430, Tokyo, Japan · Informatics Program, Graduate Institute for Advanced Studies (SOKENDAI), 2-1-2 Hitotsubashi, Chiyoda-ku, 101-8430, Tokyo, Japan

Temporal-Difference Learning Robust RL Actor-Critic Methods

Apr 1, 2026

Full-Gradient Successor Feature Representations

Successor Features (SF) combined with Generalized Policy Improvement (GPI) provide a robust framework for transfer learning in Reinforcement Learning (RL) by decoupling environment dynamics from reward functions. However, standard SF learning methods typically rely on semi-gradient Temporal Difference (TD) updates. When combined with non-linear function approximation, semi-gradient methods lack robust convergence guarantees and can lead to instability, particularly in the multi-task setting where accurate feature estimation is critical for effective GPI. Inspired by Full Gradient DQN, we propose Full-Gradient Successor Feature Representations Q-Learning (FG-SFRQL), an algorithm that optimizes the successor features by minimizing the full Mean Squared Bellman Error. Unlike standard approaches, our method computes gradients with respect to parameters in both the online and target networks. We provide a theoretical proof of almost-sure convergence for FG-SFRQL and demonstrate empirically that minimizing the full residual leads to superior sample efficiency and transfer performance compared to semi-gradient baselines in both discrete and continuous domains.

Ritish Shrirao, Aditya Priyadarshi, Raghuram Bharadwaj Diddigi

Dept. of CSE, IIIT Bangalore · Dept. of DSAI, IIIT Bangalore

Reinforcement Learning Successor Representations Temporal-Difference Learning Multi-Task RL

Mar 29, 2026

Stability and Sensitivity Analysis of Relative Temporal-Difference Learning: Extended Version

Relative temporal-difference (TD) learning was introduced to mitigate the slow convergence of TD methods when the discount factor approaches one by subtracting a baseline from the temporal-difference update. While this idea has been studied in the tabular setting, stability guarantees with function approximation remain poorly understood. This paper analyzes relative TD learning with linear function approximation. We establish stability conditions for the algorithm and show that the choice of baseline distribution plays a central role. In particular, when the baseline is chosen as the empirical distribution of the state-action process, the algorithm is stable for any non-negative baseline weight and any discount factor. We also provide a sensitivity analysis of the resulting parameter estimates, characterizing both asymptotic bias and covariance. The asymptotic covariance and asymptotic bias are shown to remain uniformly bounded as the discount factor approaches one.

Masoud S. Sakha, Rushikesh Kamalapurkar, Sean Meyn

Temporal-Difference Learning

Mar 23, 2026

Deep Reinforcement Learning and The Tale of Two Temporal Difference Errors

The temporal difference (TD) error was first formalized in Sutton (1988), where it was first characterized as the difference between temporally successive predictions, and later, in that same work, formulated as the difference between a bootstrapped target and a prediction. Since then, these two interpretations of the TD error have been used interchangeably in the literature, with the latter eventually being adopted as the standard critic loss in deep reinforcement learning (RL) architectures. In this work, we show that these two interpretations of the TD error are not always equivalent. In particular, we show that increasingly-nonlinear deep RL architectures can cause these interpretations of the TD error to yield increasingly different numerical values. Then, building on this insight, we show how choosing one interpretation of the TD error over the other can affect the performance of deep RL algorithms that utilize the TD error to compute other quantities, such as with deep differential (i.e., average-reward) RL methods. All in all, our results show that the default interpretation of the TD error as the difference between a bootstrapped target and a prediction does not always hold in deep RL settings.

Juan Sebastian Rojas, Chi-Guhn Lee

University of Toronto, Canada

Temporal-Difference Learning

Mar 14, 2026

Chunk-Guided Q-Learning

In offline reinforcement learning (RL), single-step temporal-difference (TD) learning can suffer from bootstrapping error accumulation over long horizons. Action-chunked TD methods mitigate this by backing up over multiple steps, but can introduce suboptimality by restricting the policy class to open-loop action sequences. To resolve this trade-off, we present Chunk-Guided Q-Learning (CGQ), a single-step TD algorithm that guides a fine-grained single-step critic by regularizing it toward a chunk-based critic trained using temporally extended backups. This reduces compounding error while preserving fine-grained value propagation. We theoretically show that CGQ attains tighter critic optimality bounds than either single-step or action-chunked TD learning alone. Empirically, CGQ achieves strong performance on challenging long-horizon OGBench tasks, often outperforming both single-step and action-chunked methods.

Gwanwoo Song, Kwanyoung Park, Youngwoon Lee

Department of Artificial Intelligence, Yonsei University · UC Berkeley

Reinforcement Learning Q-Learning Temporal-Difference Learning Offline RL

Mar 8, 2026

Gradient Iterated Temporal-Difference Learning

Temporal-difference (TD) learning is highly effective at controlling and evaluating an agent's long-term outcomes. Most approaches in this paradigm implement a semi-gradient update to boost the learning speed, which consists of ignoring the gradient of the bootstrapped estimate. While popular, this type of update is prone to divergence, as Baird's counterexample illustrates. Gradient TD methods were introduced to overcome this issue, but have not been widely used, potentially due to issues with learning speed compared to semi-gradient methods. Recently, iterated TD learning was developed to increase the learning speed of TD methods. For that, it learns a sequence of action-value functions in parallel, where each function is optimized to represent the application of the Bellman operator over the previous function in the sequence. While promising, this algorithm can be unstable due to its semi-gradient nature, as each function tracks a moving target. In this work, we modify iterated TD learning by computing the gradients over those moving targets, aiming to build a powerful gradient TD method that competes with semi-gradient methods. Our evaluation reveals that this algorithm, called Gradient Iterated Temporal-Difference learning, has a competitive learning speed against semi-gradient methods across various benchmarks, including Atari games, a result that no prior work on gradient TD methods has demonstrated.

Théo Vincent, Kevin Gerhardt, Yogesh Tripathi +5

DFKI · TU Darmstadt · Alberta Machine Intelligence Institute (Amii) +4

Temporal-Difference Learning

Mar 4, 2026

What Does Flow Matching Bring To TD Learning?

Recent work shows that flow matching can be effective for scalar Q-value function estimation in reinforcement learning (RL), but it remains unclear why or how this approach differs from standard critics. Contrary to conventional belief, we show that their success is not explained by distributional RL, as explicitly modeling return distributions can reduce performance. Instead, we argue that the use of integration for reading out values and dense velocity supervision at each step of this integration process for training improves TD learning via two mechanisms. First, it enables robust value prediction through test-time recovery, whereby iterative computation through integration dampens errors in early value estimates as more integration steps are performed. This recovery mechanism is absent in monolithic critics. Second, supervising the velocity field at multiple interpolant values induces more plastic feature learning within the network, allowing critics to represent non-stationary TD targets without discarding previously learned features or overfitting to individual TD targets encountered during training. We formalize these effects and validate them empirically, showing that flow-matching critics substantially outperform monolithic critics (2

\times

in final performance and around 5

\times

in sample efficiency) in settings where loss of plasticity poses a challenge e.g., in high-UTD online RL problems, while remaining stable during learning.

Bhavya Agrawalla, Michal Nauman, Aviral Kumar

Carnegie Mellon University · University of Warsaw

Reinforcement Learning Value Function Estimation Temporal-Difference Learning

Mar 3, 2026

Towards Parameter-Free Temporal Difference Learning

Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However, they often require setting the algorithm parameters using problem-dependent quantities that are difficult to estimate in practice -- such as the minimum eigenvalue of the feature covariance (

ω

) or the mixing time of the underlying Markov chain (

τ_{\text{mix}}

). In addition, some analyses rely on nonstandard and impractical modifications, exacerbating the gap between theory and practice. To address these limitations, we use an exponential step-size schedule with the standard TD(0) algorithm. We analyze the resulting method under two sampling regimes: independent and identically distributed (i.i.d.) sampling from the stationary distribution, and the more practical Markovian sampling along a single trajectory. In the i.i.d.\ setting, the proposed algorithm does not require knowledge of problem-dependent quantities such as

ω

, and attains the optimal bias-variance trade-off for the last iterate. In the Markovian setting, we propose a regularized TD(0) algorithm with an exponential step-size schedule. The resulting algorithm achieves a comparable convergence rate to prior works, without requiring projections, iterate averaging, or knowledge of

τ_{\text{mix}}

or

ω

.

Yunxiang Li, Mark Schmidt, Reza Babanezhad +1

University of British Columbia · Samsung AI - Montreal · Simon Fraser University

Temporal-Difference Learning

Mar 2, 2026

Personalized Multi-Agent Average Reward TD-Learning via Joint Linear Approximation

We study personalized multi-agent average reward TD learning, in which a collection of agents interacts with different environments and jointly learns their respective value functions. We focus on the setting where there exists a shared linear representation, and the agents' optimal weights collectively lie in an unknown linear subspace. Inspired by the recent success of personalized federated learning (PFL), we study the convergence of cooperative single-timescale TD learning in which agents iteratively estimate the common subspace and local heads. We showed that this decomposition can filter out conflicting signals, effectively mitigating the negative impacts of ``misaligned'' signals, and achieving linear speedup. The main technical challenges lie in the heterogeneity, the Markovian sampling, and their intricate interplay in shaping error evolutions. Specifically, not only are the error dynamics of multiple variables closely interconnected, but there is also no direct contraction for the principal angle distance between the optimal subspace and the estimated subspace. We hope our analytical techniques can be useful to inspire research on deeper exploration into leveraging common structures. Experiments are provided to show the benefits of learning via a shared structure to the more general control problem.

Leo Muxing Wang, Pengkun Yang, Lili Su

Northeastern University · Tsinghua University

Temporal-Difference Learning Multi-Agent Reinforcement Learning Cooperative MARL Average-Reward RL Linear Function Approximation

Feb 18, 2026

Almost Sure Convergence of Differential Temporal Difference Learning for Average Reward Markov Decision Processes

The average reward is a fundamental performance metric in reinforcement learning (RL) focusing on the long-run performance of an agent. Differential temporal difference (TD) learning algorithms are a major advance for average reward RL as they provide an efficient online method to learn the value functions associated with the average reward in both on-policy and off-policy settings. However, existing convergence guarantees require a local clock in learning rates tied to state visit counts, which practitioners do not use and does not extend beyond tabular settings. We address this limitation by proving the almost sure convergence of on-policy

n

-step differential TD for any

n

using standard diminishing learning rates without a local clock. We then derive three sufficient conditions under which off-policy

n

-step differential TD also converges without a local clock. These results strengthen the theoretical foundations of differential TD and bring its convergence analysis closer to practical implementations.

Ethan Blaser, Jiuqi Wang, Shangtong Zhang

University of Virginia

Temporal-Difference Learning Average-Reward RL Off-Policy RL

Feb 2, 2026

Finite-Sample Wasserstein Error Bounds and Concentration Inequalities for Nonlinear Stochastic Approximation

Stochastic approximation methods such as stochastic gradient descent and temporal-difference learning return either the last iterate or the Polyak--Ruppert average. We establish finite-sample Wasserstein-

p

Gaussian approximation bounds for both outputs under a common framework combining moment bounds for the normalized iterates with quantitative Gaussian approximation of the appropriately weighted driving noise. These bounds yield convergence of admissible moments and high probability bounds with Gaussian leading terms: heavier dependence on the confidence level is confined to a correction that vanishes with the sample size. We verify the framework's conditions for nonlinear stochastic approximation with independent or Markovian observations and linear stochastic approximation with Markovian observations, with applications to stochastic gradient descent and temporal-difference learning.

Seo Taek Kong, R. Srikant

University of Illinois Urbana-Champaign

Stochastic Approximation Stochastic Gradient Descent Temporal-Difference Learning

Jun 6, 2025

Ensemble Elastic DQN: A Step Dependent Ensemble Approach for Reducing Overestimation in Deep Value-Based Reinforcement Learning

Deep Q-Networks (DQN) can suffer from overestimation bias because bootstrapped targets use a maximisation operation over noisy value estimates. Ensemble-based methods and multi-step methods have each been used to improve the stability and sample efficiency of value-based reinforcement learning, but their interaction remains less well understood. This paper introduces Ensemble Elastic DQN (EEDQN), a value-based reinforcement learning algorithm that combines adaptive elastic multi-step returns with ensemble-based target aggregation. EEDQN replaces the clustering-based state similarity test used in earlier Elastic Step DQN with a lightweight Q-value difference rule, making adaptive return construction simpler to apply in discrete control settings. The method then applies horizon dependent ensemble aggregation, one-step targets use the ensemble mean, while longer elastic returns use the ensemble minimum. This design aims to reduce extreme optimistic bootstrap estimates without making every update uniformly conservative. We evaluate EEDQN on five MinAtar environments against DQN, Double DQN, Averaged DQN, MaxMin DQN, and Elastic Step DQN. EEDQN achieves the highest final return in four of the five environments and remains competitive with conservative ensemble baselines. An aggregation rule ablation shows that the best degree of conservatism is environment dependent, suggesting that adaptive return length and ensemble aggregation interact in non-trivial ways.

Adrian Ly, Richard Dazeley, Peter Vamplew +2

Reinforcement Learning Deep Q-Learning Temporal-Difference Learning

Mar 24, 2025

Reinforcement Learning in Switching Non-Stationary Markov Decision Processes: Algorithms and Convergence Analysis

We introduce the Switching Non-Stationary Markov Decision Process (SNS-MDP) framework, in which the environment transitions among a finite set of MDPs governed by a latent Markov chain while the agent observes only the external state. We show that the long-term effect of this switching is equivalent to stationary dynamics parameterized by the stationary distribution of the hidden Markov chain. For fixed policies, we derive a closed-form expression for the SNS value function and prove that standard temporal-difference (TD) learning converges to it almost surely despite persistent non-stationarity. We further establish that policy iteration converges to the optimal policy of the equivalent averaged environment, and prove that tabular Q-learning converges almost surely to the optimal Q-function. The framework is validated on a wireless communication network with Markovian channel noise, demonstrating its practical efficacy for decision-making in rapidly time-varying systems.

Mohsen Amiri, Sindri Magnússon

Department of Computer and System Science, Stockholm University, SE-164 25 Stockholm, Sweden

Non-Stationary RL Markov Decision Processes Markov Models Q-Learning Temporal-Difference Learning

Nov 14, 2024

Temporal difference learning adapts to incomplete coverage: an oracle inequality over subgraphs

Temporal difference (TD) and Monte Carlo (MC) are two fundamental principles for value function estimation in reinforcement learning. TD is asymptotically efficient for value estimation, whereas MC requires only adequate target visitation. We show that these advantages are automatically combined by ordinary TD in the tabular setting. We identify the subgraph Bellman variance, arising from bootstrapping within a subgraph and rollouts outside it, as a fundamental quantity connecting the MC and efficient TD benchmarks. With independent trajectories, we prove a non-asymptotic oracle inequality: the mean squared error of full TD is bounded by this variance divided by the sample size for every sufficiently covered subgraph containing the target, up to a higher-order remainder whose occupancy dependence is confined to that subgraph. No subgraph is supplied to the algorithm. TD thus adapts without selecting a subgraph or requiring global coverage. A finite-sample minimax lower bound shows that the asymptotic variance of TD need not be attainable before rare states are adequately observed. Experimental studies examine the transition between these variance scales and its dependence on visitation structure.

Wenlong Mou, Jian Qian

Department of Statistical Sciences, University of Toronto · Department of EECS, Massachusetts Institute of Technology

Temporal-Difference Learning Reinforcement Learning Value Function Estimation

Oct 21, 2024

Statistical Inference for Policy Evaluation with Temporal Difference Learning

We investigate the statistical properties of Temporal Difference (TD) learning with Polyak-Ruppert averaging, arguably one of the most widely used algorithms in reinforcement learning, for the task of estimating the parameters of the optimal linear approximation to the value function. Assuming independent samples, we make three theoretical contributions that improve upon the current state-of-the-art results: (i) we establish refined high-dimensional Berry-Esseen bounds over the class of convex sets, achieving faster rates than the best known results, and (ii) we propose and analyze a novel, computationally efficient online plug-in estimator of the asymptotic covariance matrix; (iii) we derive sharper high probability convergence guarantees that depend explicitly on the asymptotic variance and hold under weaker conditions than those adopted in the literature. These results enable the construction of confidence regions and simultaneous confidence intervals for the linear parameters of the value function approximation, with guaranteed finite-sample coverage. We demonstrate the applicability of our theoretical findings through numerical experiments.

Weichen Wu, Gen Li, Yuting Wei +1

The Voleon Group, New York, NY, USA · Department of Statistics, The Chinese University of Hong Kong, Hong Kong SAR. · Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, Philadelphia, PA, USA. +1

Parameter Estimation Confidence Region Estimation Value Function Estimation Stochastic Approximation Policy Evaluation Temporal-Difference Learning+3

Oct 9, 2024

Deep End-to-End Survival Analysis with Temporal Consistency

In this study, we present a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data. Our approach draws inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm, extending Temporal Learning concepts to Survival Regression. A central argument in our method relies on temporal consistency, a recursive consistency condition between survival predictions made at consecutive states. Our framework introduces a delayed target network that decouples the generation of temporally consistent training targets from model updates, providing a more stable training signal while enabling mini-batch optimization and end-to-end training. Additionally, it supports arbitrarily complex architectures, enabling the modeling of intricate temporal dependencies. Through numerous experiments we provide empirical evidence demonstrating our framework's ability to exploit temporal consistency across datasets of varying sizes. Moreover, our algorithm outperforms benchmarks on datasets with long sequences, demonstrating its ability to capture long-term patterns. Finally, ablation studies show that the degree of target delay has a substantial effect on predictive performance and training variability. Across two distinct survival model families, delayed target updates consistently improve over the same-timescale baseline.

Mariana Vargas Vieyra, Pascal Frossard

EPFL

Survival Analysis Temporal Consistency Temporal-Difference Learning