# Why Target Networks Stabilise Temporal Difference Methods

## TL;DR

This paper provides a theoretical explanation for why target networks stabilize temporal difference learning in deep reinforcement learning, showing they mitigate poor conditioning and can guarantee convergence under certain conditions.

## Contribution

It formalizes the concept of partially fitted policy evaluation, characterizes the deadly triad, and explains how target networks improve stability and convergence in complex RL settings.

## Key findings

- Target networks mitigate poor conditioning in TD updates.
- Proper tuning of target network update frequency ensures convergence.
- The framework bridges fitted methods and semigradient TD algorithms.

## Abstract

Integral to recent successes in deep reinforcement learning has been a class of temporal difference methods that use infrequently updated target values for policy evaluation in a Markov Decision Process. Yet a complete theoretical explanation for the effectiveness of target networks remains elusive. In this work, we provide an analysis of this popular class of algorithms, to finally answer the question: `why do target networks stabilise TD learning'? To do so, we formalise the notion of a partially fitted policy evaluation method, which describes the use of target networks and bridges the gap between fitted methods and semigradient temporal difference algorithms. Using this framework we are able to uniquely characterise the so-called deadly triad - the use of TD updates with (nonlinear) function approximation and off-policy data - which often leads to nonconvergent algorithms. This insight leads us to conclude that the use of target networks can mitigate the effects of poor conditioning in the Jacobian of the TD update. Instead, we show that under mild regularity conditions and a well tuned target network update frequency, convergence can be guaranteed even in the extremely challenging off-policy sampling and nonlinear function approximation setting.