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Register a new userFinite Sample Analyses for TD(0) with Function Approximation
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Gal Dalal
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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TD(0) is one of the most commonly used algorithms in reinforcement learning. Despite this, there is no existing finite sample analysis for TD(0) with function approximation, even for the linear case. Our work is the first to provide such results. Existing convergence rates for Temporal Difference (TD) methods apply only to somewhat modifi
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Two-timescale Stochastic Approximation (SA) algorithms are widely used in Reinforcement Learning (RL). Their iterates have two parts that are updated using distinct stepsizes. In this work, we develop a novel recipe for their finite sample analysis. Using this, we provide a concentration bound, which is the first such result for a two-timescale SA. The type of bound we obtain is known as `lock-in probability. We also introduce a new projection scheme, in which the time between successive projections increases exponentially. This scheme allows one to elegantly transform a lock-in probability into a convergence rate result for projected two-timescale SA. From this latter result, we then extract key insights on stepsize selection. As an application, we finally obtain convergence rates for the projected two-timescale RL algorithms GTD(0), GTD2, and TDC.
Motivated by the emerging use of multi-agent reinforcement learning (MARL) in engineering applications such as networked robotics, swarming drones, and sensor networks, we investigate the policy evaluation problem in a fully decentralized setting, using temporal-difference (TD) learning with linear function approximation to handle large state spaces in practice. The goal of a group of agents is to collaboratively learn the value function of a given policy from locally private rewards observed in a shared environment, through exchanging local estimates with neighbors. Despite their simplicity and widespread use, our theoretical understanding of such decentralized TD learning algorithms remains limited. Existing results were obtained based on i.i.d. data samples, or by imposing an `additional projection step to control the `gradient bias incurred by the Markovian observations. In this paper, we provide a finite-sample analysis of the fully decentralized TD(0) learning under both i.i.d. as well as Markovian samples, and prove that all local estimates converge linearly to a small neighborhood of the optimum. The resultant error bounds are the first of its type---in the sense that they hold under the most practical assumptions ---which is made possible by means of a novel multi-step Lyapunov analysis.
The current state-of-the-art Scrabble agents are not learning-based but depend on truncated Monte Carlo simulations and the quality of such agents is contingent upon the time available for running the simulations. This thesis takes steps towards building a learning-based Scrabble agent using self-play. Specifically, we try to find a better function approximation for the static evaluation function used in Scrabble which determines the move goodness at a given board configuration. In this work, we experimented with evolutionary algorithms and Bayesian Optimization to learn the weights for an approximate feature-based evaluation function. However, these optimization methods were not quite effective, which lead us to explore the given problem from an Imitation Learning point of view. We also tried to imitate the ranking of moves produced by the Quackle simulation agent using supervised learning with a neural network function approximator which takes the raw representation of the Scrabble board as the input instead of using only a fixed number of handcrafted features.
We provide a new non-asymptotic analysis of distributed TD(0) with linear function approximation. Our approach relies on one-shot averaging, where $N$ agents run local copies of TD(0) and average the outcomes only once at the very end. We consider two models: one in which the agents interact with an environment they can observe and whose transitions depends on all of their actions (which we call the global state model), and one in which each agent can run a local copy of an identical Markov Decision Process, which we call the local state model. In the global state model, we show that the convergence rate of our distributed one-shot averaging method matches the known convergence rate of TD(0). By contrast, the best convergence rate in the previous literature showed a rate which, in the worst case, underperformed the non-distributed version by $O(N^3)$ in terms of the number of agents $N$. In the local state model, we demonstrate a version of the linear time speedup phenomenon, where the convergence time of the distributed process is a factor of $N$ faster than the convergence time of TD(0). As far as we are aware, this is the first result rigorously showing benefits from parallelism for temporal difference methods.
Multi-step temporal-difference (TD) learning, where the update targets contain information from multiple time steps ahead, is one of the most popular forms of TD learning for linear function approximation. The reason is that multi-step methods often yield substantially better performance than their single-step counter-parts, due to a lower bias of the update targets. For non-linear function approximation, however, single-step methods appear to be the norm. Part of the reason could be that on many domains the popular multi-step methods TD($lambda$) and Sarsa($lambda$) do not perform well when combined with non-linear function approximation. In particular, they are very susceptible to divergence of value estimates. In this paper, we identify the reason behind this. Furthermore, based on our analysis, we propose a new multi-step TD method for non-linear function approximation that addresses this issue. We confirm the effectiveness of our method using two benchmark tasks with neural networks as function approximation.
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