# PID Accelerated Temporal Difference Algorithms

arXiv: https://arxiv.org/abs/2407.08803 · HTML: https://mlsanity.com/paper/2407.08803/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 14 of 14)

- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Stochastic approximation with cone-contractive operators: Sharp ℓ_∞-bounds for Q-learning](https://mlsanity.com/paper/1905.06265/) (2019)
- [Momentum in Reinforcement Learning](https://mlsanity.com/paper/1910.09322/) (2019)
- [Finite-Sample Analysis of Stochastic Approximation Using Smooth Convex Envelopes](https://mlsanity.com/paper/2002.00874/) (2020)
- [A First-Order Approach To Accelerated Value Iteration](https://mlsanity.com/paper/1905.09963/) (2019)
- [Anderson Acceleration for Reinforcement Learning](https://mlsanity.com/paper/1809.09501/) (2018)
- [Zap Q-Learning With Nonlinear Function Approximation](https://mlsanity.com/paper/1910.05405/) (2019)
- [Accelerating Value Iteration with Anchoring](https://mlsanity.com/paper/2305.16569/) (2023)
- [Operator Splitting Value Iteration](https://mlsanity.com/paper/2211.13937/) (2022)
- [A History of Meta-gradient: Gradient Methods for Meta-learning](https://mlsanity.com/paper/2202.09701/) (2022)
- [TIDBD: Adapting Temporal-difference Step-sizes Through Stochastic Meta-descent](https://mlsanity.com/paper/1804.03334/) (2018)
- [Maximum Entropy Model Correction in Reinforcement Learning](https://mlsanity.com/paper/2311.17855/) (2023)

## Built on by (most cited first, 2 of 2)

- [Deflated Dynamics Value Iteration](https://mlsanity.com/paper/2407.10454/) (2024)
- [Control and Reinforcement Learning through the Lens of Optimization: An Algorithmic Perspective](https://mlsanity.com/paper/2512.07377/) (2025)

## Abstract (arXiv)

Long-horizon tasks, which have a large discount factor, pose a challenge for most conventional reinforcement learning (RL) algorithms. Algorithms such as Value Iteration and Temporal Difference (TD) learning have a slow convergence rate and become inefficient in these tasks. When the transition distributions are given, PID VI was recently introduced to accelerate the convergence of Value Iteration using ideas from control theory. Inspired by this, we introduce PID TD Learning and PID Q-Learning algorithms for the RL setting, in which only samples from the environment are available. We give a theoretical analysis of the convergence of PID TD Learning and its acceleration compared to the conventional TD Learning. We also introduce a method for adapting PID gains in the presence of noise and empirically verify its effectiveness.