arXiv subjects

Richard S. Sutton

Publications and source records attributed to Richard S. Sutton.

At least 55 records · Page 3Linked to original sources

arXiv2019

Discounted Reinforcement Learning Is Not an Optimization Problem

Discounted reinforcement learning is fundamentally incompatible with function approximation for control in continuing tasks. It is not an optimization problem in its usual formulation, so when using function approximation there is no optimal policy. We substantiate these claims, then go on to address some misconceptions about discounting and its connection to the average reward formulation. We encourage researchers to adopt rigorous optimization approaches, such as maximizing average reward, for reinforcement learning in continuing tasks.

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arXiv2019

Learning Feature Relevance Through Step Size Adaptation in Temporal-Difference Learning

There is a long history of using meta learning as representation learning, specifically for determining the relevance of inputs. In this paper, we examine an instance of meta-learning in which feature relevance is learned by adapting step size parameters of stochastic gradient descent---building on a variety of prior work in stochastic approximation, machine learning, and artificial neural networks. In particular, we focus on stochastic meta-descent introduced in the Incremental Delta-Bar-Delta (IDBD) algorithm for setting individual step sizes for each feature of a linear function approximator. Using IDBD, a feature with large or small step sizes will have a large or small impact on generalization from training examples. As a main contribution of this work, we extend IDBD to temporal-difference (TD) learning---a form of learning which is effective in sequential, non i.i.d. problems. We derive a variety of IDBD generalizations for TD learning, demonstrating that they are able to distinguish which features are relevant and which are not. We demonstrate that TD IDBD is effective at learning feature relevance in both an idealized gridworld and a real-world robotic prediction task.

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arXiv2019

Should All Temporal Difference Learning Use Emphasis?

Emphatic Temporal Difference (ETD) learning has recently been proposed as a convergent off-policy learning method. ETD was proposed mainly to address convergence issues of conventional Temporal Difference (TD) learning under off-policy training but it is different from conventional TD learning even under on-policy training. A simple counterexample provided back in 2017 pointed to a potential class of problems where ETD converges but TD diverges. In this paper, we empirically show that ETD converges on a few other well-known on-policy experiments whereas TD either diverges or performs poorly. We also show that ETD outperforms TD on the mountain car prediction problem. Our results, together with a similar pattern observed under off-policy training in prior works, suggest that ETD might be a good substitute over conventional TD.

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arXiv2019

Understanding Multi-Step Deep Reinforcement Learning: A Systematic Study of the DQN Target

Multi-step methods such as Retrace($λ$) and $n$-step $Q$-learning have become a crucial component of modern deep reinforcement learning agents. These methods are often evaluated as a part of bigger architectures and their evaluations rarely include enough samples to draw statistically significant conclusions about their performance. This type of methodology makes it difficult to understand how particular algorithmic details of multi-step methods influence learning. In this paper we combine the $n$-step action-value algorithms Retrace, $Q$-learning, Tree Backup, Sarsa, and $Q(σ)$ with an architecture analogous to DQN. We test the performance of all these algorithms in the mountain car environment; this choice of environment allows for faster training times and larger sample sizes. We present statistical analyses on the effects of the off-policy correction, the backup length parameter $n$, and the update frequency of the target network on the performance of these algorithms. Our results show that (1) using off-policy correction can have an adverse effect on the performance of Sarsa and $Q(σ)$; (2) increasing the backup length $n$ consistently improved performance across all the different algorithms; and (3) the performance of Sarsa and $Q$-learning was more robust to the effect of the target network update frequency than the performance of Tree Backup, $Q(σ)$, and Retrace in this particular task.

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arXiv2018

Online Off-policy Prediction

This paper investigates the problem of online prediction learning, where learning proceeds continuously as the agent interacts with an environment. The predictions made by the agent are contingent on a particular way of behaving, represented as a value function. However, the behavior used to select actions and generate the behavior data might be different from the one used to define the predictions, and thus the samples are generated off-policy. The ability to learn behavior-contingent predictions online and off-policy has long been advocated as a key capability of predictive-knowledge learning systems but remained an open algorithmic challenge for decades. The issue lies with the temporal difference (TD) learning update at the heart of most prediction algorithms: combining bootstrapping, off-policy sampling and function approximation may cause the value estimate to diverge. A breakthrough came with the development of a new objective function that admitted stochastic gradient descent variants of TD. Since then, many sound online off-policy prediction algorithms have been developed, but there has been limited empirical work investigating the relative merits of all the variants. This paper aims to fill these empirical gaps and provide clarity on the key ideas behind each method. We summarize the large body of literature on off-policy learning, focusing on 1- methods that use computation linear in the number of features and are convergent under off-policy sampling, and 2- other methods which have proven useful with non-fixed, nonlinear function approximation. We provide an empirical study of off-policy prediction methods in two challenging microworlds. We report each method's parameter sensitivity, empirical convergence rate, and final performance, providing new insights that should enable practitioners to successfully extend these new methods to large-scale applications.[Abridged abstract]

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arXiv2018

On Generalized Bellman Equations and Temporal-Difference Learning

We consider off-policy temporal-difference (TD) learning in discounted Markov decision processes, where the goal is to evaluate a policy in a model-free way by using observations of a state process generated without executing the policy. To curb the high variance issue in off-policy TD learning, we propose a new scheme of setting the $λ$-parameters of TD, based on generalized Bellman equations. Our scheme is to set $λ$ according to the eligibility trace iterates calculated in TD, thereby easily keeping these traces in a desired bounded range. Compared with prior work, this scheme is more direct and flexible, and allows much larger $λ$ values for off-policy TD learning with bounded traces. As to its soundness, using Markov chain theory, we prove the ergodicity of the joint state-trace process under nonrestrictive conditions, and we show that associated with our scheme is a generalized Bellman equation (for the policy to be evaluated) that depends on both the evolution of $λ$ and the unique invariant probability measure of the state-trace process. These results not only lead immediately to a characterization of the convergence behavior of least-squares based implementation of our scheme, but also prepare the ground for further analysis of gradient-based implementations.

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arXiv2018

Predicting Periodicity with Temporal Difference Learning

Temporal difference (TD) learning is an important approach in reinforcement learning, as it combines ideas from dynamic programming and Monte Carlo methods in a way that allows for online and incremental model-free learning. A key idea of TD learning is that it is learning predictive knowledge about the environment in the form of value functions, from which it can derive its behavior to address long-term sequential decision making problems. The agent's horizon of interest, that is, how immediate or long-term a TD learning agent predicts into the future, is adjusted through a discount rate parameter. In this paper, we introduce an alternative view on the discount rate, with insight from digital signal processing, to include complex-valued discounting. Our results show that setting the discount rate to appropriately chosen complex numbers allows for online and incremental estimation of the Discrete Fourier Transform (DFT) of a signal of interest with TD learning. We thereby extend the types of knowledge representable by value functions, which we show are particularly useful for identifying periodic effects in the reward sequence.

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arXiv2018

Two geometric input transformation methods for fast online reinforcement learning with neural nets

We apply neural nets with ReLU gates in online reinforcement learning. Our goal is to train these networks in an incremental manner, without the computationally expensive experience replay. By studying how individual neural nodes behave in online training, we recognize that the global nature of ReLU gates can cause undesirable learning interference in each node's learning behavior. We propose reducing such interferences with two efficient input transformation methods that are geometric in nature and match well the geometric property of ReLU gates. The first one is tile coding, a classic binary encoding scheme originally designed for local generalization based on the topological structure of the input space. The second one (EmECS) is a new method we introduce; it is based on geometric properties of convex sets and topological embedding of the input space into the boundary of a convex set. We discuss the behavior of the network when it operates on the transformed inputs. We also compare it experimentally with some neural nets that do not use the same input transformations, and with the classic algorithm of tile coding plus a linear function approximator, and on several online reinforcement learning tasks, we show that the neural net with tile coding or EmECS can achieve not only faster learning but also more accurate approximations. Our results strongly suggest that geometric input transformation of this type can be effective for interference reduction and takes us a step closer to fully incremental reinforcement learning with neural nets.

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arXiv2018

Per-decision Multi-step Temporal Difference Learning with Control Variates

Multi-step temporal difference (TD) learning is an important approach in reinforcement learning, as it unifies one-step TD learning with Monte Carlo methods in a way where intermediate algorithms can outperform either extreme. They address a bias-variance trade off between reliance on current estimates, which could be poor, and incorporating longer sampled reward sequences into the updates. Especially in the off-policy setting, where the agent aims to learn about a policy different from the one generating its behaviour, the variance in the updates can cause learning to diverge as the number of sampled rewards used in the estimates increases. In this paper, we introduce per-decision control variates for multi-step TD algorithms, and compare them to existing methods. Our results show that including the control variates can greatly improve performance on both on and off-policy multi-step temporal difference learning tasks.

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arXiv2018

Multi-step Reinforcement Learning: A Unifying Algorithm

Unifying seemingly disparate algorithmic ideas to produce better performing algorithms has been a longstanding goal in reinforcement learning. As a primary example, TD($λ$) elegantly unifies one-step TD prediction with Monte Carlo methods through the use of eligibility traces and the trace-decay parameter $λ$. Currently, there are a multitude of algorithms that can be used to perform TD control, including Sarsa, $Q$-learning, and Expected Sarsa. These methods are often studied in the one-step case, but they can be extended across multiple time steps to achieve better performance. Each of these algorithms is seemingly distinct, and no one dominates the others for all problems. In this paper, we study a new multi-step action-value algorithm called $Q(σ)$ which unifies and generalizes these existing algorithms, while subsuming them as special cases. A new parameter, $σ$, is introduced to allow the degree of sampling performed by the algorithm at each step during its backup to be continuously varied, with Sarsa existing at one extreme (full sampling), and Expected Sarsa existing at the other (pure expectation). $Q(σ)$ is generally applicable to both on- and off-policy learning, but in this work we focus on experiments in the on-policy case. Our results show that an intermediate value of $σ$, which results in a mixture of the existing algorithms, performs better than either extreme. The mixture can also be varied dynamically which can result in even greater performance.

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arXiv2018

Integrating Episodic Memory into a Reinforcement Learning Agent using Reservoir Sampling

Episodic memory is a psychology term which refers to the ability to recall specific events from the past. We suggest one advantage of this particular type of memory is the ability to easily assign credit to a specific state when remembered information is found to be useful. Inspired by this idea, and the increasing popularity of external memory mechanisms to handle long-term dependencies in deep learning systems, we propose a novel algorithm which uses a reservoir sampling procedure to maintain an external memory consisting of a fixed number of past states. The algorithm allows a deep reinforcement learning agent to learn online to preferentially remember those states which are found to be useful to recall later on. Critically this method allows for efficient online computation of gradient estimates with respect to the write process of the external memory. Thus unlike most prior mechanisms for external memory it is feasible to use in an online reinforcement learning setting.

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arXiv2018

A Deeper Look at Experience Replay

Recently experience replay is widely used in various deep reinforcement learning (RL) algorithms, in this paper we rethink the utility of experience replay. It introduces a new hyper-parameter, the memory buffer size, which needs carefully tuning. However unfortunately the importance of this new hyper-parameter has been underestimated in the community for a long time. In this paper we did a systematic empirical study of experience replay under various function representations. We showcase that a large replay buffer can significantly hurt the performance. Moreover, we propose a simple O(1) method to remedy the negative influence of a large replay buffer. We showcase its utility in both simple grid world and challenging domains like Atari games.

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arXiv2018

TIDBD: Adapting Temporal-difference Step-sizes Through Stochastic Meta-descent

In this paper, we introduce a method for adapting the step-sizes of temporal difference (TD) learning. The performance of TD methods often depends on well chosen step-sizes, yet few algorithms have been developed for setting the step-size automatically for TD learning. An important limitation of current methods is that they adapt a single step-size shared by all the weights of the learning system. A vector step-size enables greater optimization by specifying parameters on a per-feature basis. Furthermore, adapting parameters at different rates has the added benefit of being a simple form of representation learning. We generalize Incremental Delta Bar Delta (IDBD)---a vectorized adaptive step-size method for supervised learning---to TD learning, which we name TIDBD. We demonstrate that TIDBD is able to find appropriate step-sizes in both stationary and non-stationary prediction tasks, outperforming ordinary TD methods and TD methods with scalar step-size adaptation; we demonstrate that it can differentiate between features which are relevant and irrelevant for a given task, performing representation learning; and we show on a real-world robot prediction task that TIDBD is able to outperform ordinary TD methods and TD methods augmented with AlphaBound and RMSprop.

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arXiv2018

Reactive Reinforcement Learning in Asynchronous Environments

The relationship between a reinforcement learning (RL) agent and an asynchronous environment is often ignored. Frequently used models of the interaction between an agent and its environment, such as Markov Decision Processes (MDP) or Semi-Markov Decision Processes (SMDP), do not capture the fact that, in an asynchronous environment, the state of the environment may change during computation performed by the agent. In an asynchronous environment, minimizing reaction time---the time it takes for an agent to react to an observation---also minimizes the time in which the state of the environment may change following observation. In many environments, the reaction time of an agent directly impacts task performance by permitting the environment to transition into either an undesirable terminal state or a state where performing the chosen action is inappropriate. We propose a class of reactive reinforcement learning algorithms that address this problem of asynchronous environments by immediately acting after observing new state information. We compare a reactive SARSA learning algorithm with the conventional SARSA learning algorithm on two asynchronous robotic tasks (emergency stopping and impact prevention), and show that the reactive RL algorithm reduces the reaction time of the agent by approximately the duration of the algorithm's learning update. This new class of reactive algorithms may facilitate safer control and faster decision making without any change to standard learning guarantees.

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arXiv2018

Directly Estimating the Variance of the λ-Return Using Temporal-Difference Methods

This paper investigates estimating the variance of a temporal-difference learning agent's update target. Most reinforcement learning methods use an estimate of the value function, which captures how good it is for the agent to be in a particular state and is mathematically expressed as the expected sum of discounted future rewards (called the return). These values can be straightforwardly estimated by averaging batches of returns using Monte Carlo methods. However, if we wish to update the agent's value estimates during learning--before terminal outcomes are observed--we must use a different estimation target called the λ-return, which truncates the return with the agent's own estimate of the value function. Temporal difference learning methods estimate the expected λ-return for each state, allowing these methods to update online and incrementally, and in most cases achieve better generalization error and faster learning than Monte Carlo methods. Naturally one could attempt to estimate higher-order moments of the λ-return. This paper is about estimating the variance of the λ-return. Prior work has shown that given estimates of the variance of the λ-return, learning systems can be constructed to (1) mitigate risk in action selection, and (2) automatically adapt the parameters of the learning process itself to improve performance. Unfortunately, existing methods for estimating the variance of the λ-return are complex and not well understood empirically. We contribute a method for estimating the variance of the λ-return directly using policy evaluation methods from reinforcement learning. Our approach is significantly simpler than prior methods that independently estimate the second moment of the λ-return. Empirically our new approach behaves at least as well as existing approaches, but is generally more robust.

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arXiv2017

Communicative Capital for Prosthetic Agents

This work presents an overarching perspective on the role that machine intelligence can play in enhancing human abilities, especially those that have been diminished due to injury or illness. As a primary contribution, we develop the hypothesis that assistive devices, and specifically artificial arms and hands, can and should be viewed as agents in order for us to most effectively improve their collaboration with their human users. We believe that increased agency will enable more powerful interactions between human users and next generation prosthetic devices, especially when the sensorimotor space of the prosthetic technology greatly exceeds the conventional control and communication channels available to a prosthetic user. To more concretely examine an agency-based view on prosthetic devices, we propose a new schema for interpreting the capacity of a human-machine collaboration as a function of both the human's and machine's degrees of agency. We then introduce the idea of communicative capital as a way of thinking about the communication resources developed by a human and a machine during their ongoing interaction. Using this schema of agency and capacity, we examine the benefits and disadvantages of increasing the agency of a prosthetic limb. To do so, we present an analysis of examples from the literature where building communicative capital has enabled a progression of fruitful, task-directed interactions between prostheses and their human users. We then describe further work that is needed to concretely evaluate the hypothesis that prostheses are best thought of as agents. The agent-based viewpoint developed in this article significantly extends current thinking on how best to support the natural, functional use of increasingly complex prosthetic enhancements, and opens the door for more powerful interactions between humans and their assistive technologies.

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arXiv2017

A First Empirical Study of Emphatic Temporal Difference Learning

In this paper we present the first empirical study of the emphatic temporal-difference learning algorithm (ETD), comparing it with conventional temporal-difference learning, in particular, with linear TD(0), on on-policy and off-policy variations of the Mountain Car problem. The initial motivation for developing ETD was that it has good convergence properties under off-policy training (Sutton, Mahmood and White 2016), but it is also a new algorithm for the on-policy case. In both our on-policy and off-policy experiments, we found that each method converged to a characteristic asymptotic level of error, with ETD better than TD(0). TD(0) achieved a still lower error level temporarily before falling back to its higher asymptote, whereas ETD never showed this kind of "bounce". In the off-policy case (in which TD(0) is not guaranteed to converge), ETD was significantly slower.

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arXiv2017

GQ($λ$) Quick Reference and Implementation Guide

This document should serve as a quick reference for and guide to the implementation of linear GQ($λ$), a gradient-based off-policy temporal-difference learning algorithm. Explanation of the intuition and theory behind the algorithm are provided elsewhere (e.g., Maei & Sutton 2010, Maei 2011). If you questions or concerns about the content in this document or the attached java code please email Adam White (adam.white@ualberta.ca). The code is provided as part of the source files in the arXiv submission.

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