Finite-Time Performance Bounds and Adaptive Learning Rate Selection for Two Time-Scale Reinforcement Learning
This work addresses convergence issues in reinforcement learning algorithms, offering a practical improvement for researchers and practitioners, though it is incremental as it builds on existing methods.
The paper tackles the problem of slow convergence in two time-scale reinforcement learning algorithms like GTD, GTD2, and TDC by deriving finite-time performance bounds for fixed learning rates and using them to design an adaptive learning rate scheme, which in experiments significantly improved convergence rates over the optimal polynomial decay rule.
We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the learning rate is fixed. The key idea in obtaining these bounds is to use a Lyapunov function motivated by singular perturbation theory for linear differential equations. We use the bound to design an adaptive learning rate scheme which significantly improves the convergence rate over the known optimal polynomial decay rule in our experiments, and can be used to potentially improve the performance of any other schedule where the learning rate is changed at pre-determined time instants.