arXiv subjects

Martha White

Publications and source records attributed to Martha White.

At least 109 records · Page 6Linked to original sources

arXiv2018

High-confidence error estimates for learned value functions

Estimating the value function for a fixed policy is a fundamental problem in reinforcement learning. Policy evaluation algorithms---to estimate value functions---continue to be developed, to improve convergence rates, improve stability and handle variability, particularly for off-policy learning. To understand the properties of these algorithms, the experimenter needs high-confidence estimates of the accuracy of the learned value functions. For environments with small, finite state-spaces, like chains, the true value function can be easily computed, to compute accuracy. For large, or continuous state-spaces, however, this is no longer feasible. In this paper, we address the largely open problem of how to obtain these high-confidence estimates, for general state-spaces. We provide a high-confidence bound on an empirical estimate of the value error to the true value error. We use this bound to design an offline sampling algorithm, which stores the required quantities to repeatedly compute value error estimates for any learned value function. We provide experiments investigating the number of samples required by this offline algorithm in simple benchmark reinforcement learning domains, and highlight that there are still many open questions to be solved for this important problem.

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arXiv2018

Reinforcement Learning with Function-Valued Action Spaces for Partial Differential Equation Control

Recent work has shown that reinforcement learning (RL) is a promising approach to control dynamical systems described by partial differential equations (PDE). This paper shows how to use RL to tackle more general PDE control problems that have continuous high-dimensional action spaces with spatial relationship among action dimensions. In particular, we propose the concept of action descriptors, which encode regularities among spatially-extended action dimensions and enable the agent to control high-dimensional action PDEs. We provide theoretical evidence suggesting that this approach can be more sample efficient compared to a conventional approach that treats each action dimension separately and does not explicitly exploit the spatial regularity of the action space. The action descriptor approach is then used within the deep deterministic policy gradient algorithm. Experiments on two PDE control problems, with up to 256-dimensional continuous actions, show the advantage of the proposed approach over the conventional one.

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arXiv2018

Improving Regression Performance with Distributional Losses

There is growing evidence that converting targets to soft targets in supervised learning can provide considerable gains in performance. Much of this work has considered classification, converting hard zero-one values to soft labels---such as by adding label noise, incorporating label ambiguity or using distillation. In parallel, there is some evidence from a regression setting in reinforcement learning that learning distributions can improve performance. In this work, we investigate the reasons for this improvement, in a regression setting. We introduce a novel distributional regression loss, and similarly find it significantly improves prediction accuracy. We investigate several common hypotheses, around reducing overfitting and improved representations. We instead find evidence for an alternative hypothesis: this loss is easier to optimize, with better behaved gradients, resulting in improved generalization. We provide theoretical support for this alternative hypothesis, by characterizing the norm of the gradients of this loss.

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arXiv2018

Organizing Experience: A Deeper Look at Replay Mechanisms for Sample-based Planning in Continuous State Domains

Model-based strategies for control are critical to obtain sample efficient learning. Dyna is a planning paradigm that naturally interleaves learning and planning, by simulating one-step experience to update the action-value function. This elegant planning strategy has been mostly explored in the tabular setting. The aim of this paper is to revisit sample-based planning, in stochastic and continuous domains with learned models. We first highlight the flexibility afforded by a model over Experience Replay (ER). Replay-based methods can be seen as stochastic planning methods that repeatedly sample from a buffer of recent agent-environment interactions and perform updates to improve data efficiency. We show that a model, as opposed to a replay buffer, is particularly useful for specifying which states to sample from during planning, such as predecessor states that propagate information in reverse from a state more quickly. We introduce a semi-parametric model learning approach, called Reweighted Experience Models (REMs), that makes it simple to sample next states or predecessors. We demonstrate that REM-Dyna exhibits similar advantages over replay-based methods in learning in continuous state problems, and that the performance gap grows when moving to stochastic domains, of increasing size.

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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

Identifying global optimality for dictionary learning

Learning new representations of input observations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be difficult, in terms of efficiency and to guarantee that the solution is a global minimum. Recently, a general class of objectives have been introduced-which we term induced dictionary learning models (DLMs)-that have an induced convex form that enables global optimization. Though attractive theoretically, this induced form is impractical, particularly for large or growing datasets. In this work, we investigate the use of practical alternating minimization algorithms for induced DLMs, that ensure convergence to global optima. We characterize the stationary points of these models, and, using these insights, highlight practical choices for the objectives. We then provide theoretical and empirical evidence that alternating minimization, from a random initialization, converges to global minima for a large subclass of induced DLMs. In particular, we take advantage of the existence of the (potentially unknown) convex induced form, to identify when stationary points are global minima for the dictionary learning objective. We then provide an empirical investigation into practical optimization choices for using alternating minimization for induced DLMs, for both batch and stochastic gradient descent.

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arXiv2017

Effective sketching methods for value function approximation

High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive, particularly for matrix methods, such as least-squares temporal difference learning or quasi-Newton methods that approximate matrix step-sizes. In this work, we explore the utility of sketching for these two classes of algorithms. We highlight issues with sketching the high-dimensional features directly, which can incur significant bias. As a remedy, we demonstrate how to use sketching more sparingly, with only a left-sided sketch, that can still enable significant computational gains and the use of these matrix-based learning algorithms that are less sensitive to parameters. We empirically investigate these algorithms, in four domains with a variety of representations. Our aim is to provide insights into effective use of sketching in practice.

cs.LG↗

arXiv2017

Learning Sparse Representations in Reinforcement Learning with Sparse Coding

A variety of representation learning approaches have been investigated for reinforcement learning; much less attention, however, has been given to investigating the utility of sparse coding. Outside of reinforcement learning, sparse coding representations have been widely used, with non-convex objectives that result in discriminative representations. In this work, we develop a supervised sparse coding objective for policy evaluation. Despite the non-convexity of this objective, we prove that all local minima are global minima, making the approach amenable to simple optimization strategies. We empirically show that it is key to use a supervised objective, rather than the more straightforward unsupervised sparse coding approach. We compare the learned representations to a canonical fixed sparse representation, called tile-coding, demonstrating that the sparse coding representation outperforms a wide variety of tilecoding representations.

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arXiv2017

Accelerated Gradient Temporal Difference Learning

The family of temporal difference (TD) methods span a spectrum from computationally frugal linear methods like TD(λ) to data efficient least squares methods. Least square methods make the best use of available data directly computing the TD solution and thus do not require tuning a typically highly sensitive learning rate parameter, but require quadratic computation and storage. Recent algorithmic developments have yielded several sub-quadratic methods that use an approximation to the least squares TD solution, but incur bias. In this paper, we propose a new family of accelerated gradient TD (ATD) methods that (1) provide similar data efficiency benefits to least-squares methods, at a fraction of the computation and storage (2) significantly reduce parameter sensitivity compared to linear TD methods, and (3) are asymptotically unbiased. We illustrate these claims with a proof of convergence in expectation and experiments on several benchmark domains and a large-scale industrial energy allocation domain.

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arXiv2017

Recovering True Classifier Performance in Positive-Unlabeled Learning

A common approach in positive-unlabeled learning is to train a classification model between labeled and unlabeled data. This strategy is in fact known to give an optimal classifier under mild conditions; however, it results in biased empirical estimates of the classifier performance. In this work, we show that the typically used performance measures such as the receiver operating characteristic curve, or the precision-recall curve obtained on such data can be corrected with the knowledge of class priors; i.e., the proportions of the positive and negative examples in the unlabeled data. We extend the results to a noisy setting where some of the examples labeled positive are in fact negative and show that the correction also requires the knowledge of the proportion of noisy examples in the labeled positives. Using state-of-the-art algorithms to estimate the positive class prior and the proportion of noise, we experimentally evaluate two correction approaches and demonstrate their efficacy on real-life data.

stat.ML↗

arXiv2017

Estimating the class prior and posterior from noisy positives and unlabeled data

We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contributions remain theoretical, performing poorly on real high-dimensional data that is typically contaminated with noise. We build on this previous work to develop two practical classification algorithms that explicitly model the noise in the positive labels and utilize univariate transforms built on discriminative classifiers. We prove that these univariate transforms preserve the class prior, enabling estimation in the univariate space and avoiding kernel density estimation for high-dimensional data. The theoretical development and both parametric and nonparametric algorithms proposed here constitutes an important step towards wide-spread use of robust classification algorithms for positive-unlabeled data.

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arXiv2016

Incremental Truncated LSTD

Balancing between computational efficiency and sample efficiency is an important goal in reinforcement learning. Temporal difference (TD) learning algorithms stochastically update the value function, with a linear time complexity in the number of features, whereas least-squares temporal difference (LSTD) algorithms are sample efficient but can be quadratic in the number of features. In this work, we develop an efficient incremental low-rank LSTD(λ) algorithm that progresses towards the goal of better balancing computation and sample efficiency. The algorithm reduces the computation and storage complexity to the number of features times the chosen rank parameter while summarizing past samples efficiently to nearly obtain the sample complexity of LSTD. We derive a simulation bound on the solution given by truncated low-rank approximation, illustrating a bias- variance trade-off dependent on the choice of rank. We demonstrate that the algorithm effectively balances computational complexity and sample efficiency for policy evaluation in a benchmark task and a high-dimensional energy allocation domain.

cs.LG↗

arXiv2016

A Greedy Approach to Adapting the Trace Parameter for Temporal Difference Learning

One of the main obstacles to broad application of reinforcement learning methods is the parameter sensitivity of our core learning algorithms. In many large-scale applications, online computation and function approximation represent key strategies in scaling up reinforcement learning algorithms. In this setting, we have effective and reasonably well understood algorithms for adapting the learning-rate parameter, online during learning. Such meta-learning approaches can improve robustness of learning and enable specialization to current task, improving learning speed. For temporal-difference learning algorithms which we study here, there is yet another parameter, $λ$, that similarly impacts learning speed and stability in practice. Unfortunately, unlike the learning-rate parameter, $λ$ parametrizes the objective function that temporal-difference methods optimize. Different choices of $λ$ produce different fixed-point solutions, and thus adapting $λ$ online and characterizing the optimization is substantially more complex than adapting the learning-rate parameter. There are no meta-learning method for $λ$ that can achieve (1) incremental updating, (2) compatibility with function approximation, and (3) maintain stability of learning under both on and off-policy sampling. In this paper we contribute a novel objective function for optimizing $λ$ as a function of state rather than time. We derive a new incremental, linear complexity $λ$-adaption algorithm that does not require offline batch updating or access to a model of the world, and present a suite of experiments illustrating the practicality of our new algorithm in three different settings. Taken together, our contributions represent a concrete step towards black-box application of temporal-difference learning methods in real world problems.

cs.AI↗

arXiv2016

Investigating practical linear temporal difference learning

Off-policy reinforcement learning has many applications including: learning from demonstration, learning multiple goal seeking policies in parallel, and representing predictive knowledge. Recently there has been an proliferation of new policy-evaluation algorithms that fill a longstanding algorithmic void in reinforcement learning: combining robustness to off-policy sampling, function approximation, linear complexity, and temporal difference (TD) updates. This paper contains two main contributions. First, we derive two new hybrid TD policy-evaluation algorithms, which fill a gap in this collection of algorithms. Second, we perform an empirical comparison to elicit which of these new linear TD methods should be preferred in different situations, and make concrete suggestions about practical use.

cs.LG↗

arXiv2016

Nonparametric semi-supervised learning of class proportions

The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a previously unseen data point. This problem can be decomposed into two steps: (i) the development of accurate predictors that discriminate between positive and unlabeled data, and (ii) the accurate estimation of the prior probabilities of positive and negative examples. In this work we primarily focus on the latter subproblem. We study nonparametric class prior estimation and formulate this problem as an estimation of mixing proportions in two-component mixture models, given a sample from one of the components and another sample from the mixture itself. We show that estimation of mixing proportions is generally ill-defined and propose a canonical form to obtain identifiability while maintaining the flexibility to model any distribution. We use insights from this theory to elucidate the optimization surface of the class priors and propose an algorithm for estimating them. To address the problems of high-dimensional density estimation, we provide practical transformations to low-dimensional spaces that preserve class priors. Finally, we demonstrate the efficacy of our method on univariate and multivariate data.

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arXiv2015

Emphatic Temporal-Difference Learning

Emphatic algorithms are temporal-difference learning algorithms that change their effective state distribution by selectively emphasizing and de-emphasizing their updates on different time steps. Recent works by Sutton, Mahmood and White (2015), and Yu (2015) show that by varying the emphasis in a particular way, these algorithms become stable and convergent under off-policy training with linear function approximation. This paper serves as a unified summary of the available results from both works. In addition, we demonstrate the empirical benefits from the flexibility of emphatic algorithms, including state-dependent discounting, state-dependent bootstrapping, and the user-specified allocation of function approximation resources.

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arXiv2015

An Emphatic Approach to the Problem of Off-policy Temporal-Difference Learning

In this paper we introduce the idea of improving the performance of parametric temporal-difference (TD) learning algorithms by selectively emphasizing or de-emphasizing their updates on different time steps. In particular, we show that varying the emphasis of linear TD($λ$)'s updates in a particular way causes its expected update to become stable under off-policy training. The only prior model-free TD methods to achieve this with per-step computation linear in the number of function approximation parameters are the gradient-TD family of methods including TDC, GTD($λ$), and GQ($λ$). Compared to these methods, our _emphatic TD($λ$)_ is simpler and easier to use; it has only one learned parameter vector and one step-size parameter. Our treatment includes general state-dependent discounting and bootstrapping functions, and a way of specifying varying degrees of interest in accurately valuing different states.

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arXiv2013

Off-Policy Actor-Critic

This paper presents the first actor-critic algorithm for off-policy reinforcement learning. Our algorithm is online and incremental, and its per-time-step complexity scales linearly with the number of learned weights. Previous work on actor-critic algorithms is limited to the on-policy setting and does not take advantage of the recent advances in off-policy gradient temporal-difference learning. Off-policy techniques, such as Greedy-GQ, enable a target policy to be learned while following and obtaining data from another (behavior) policy. For many problems, however, actor-critic methods are more practical than action value methods (like Greedy-GQ) because they explicitly represent the policy; consequently, the policy can be stochastic and utilize a large action space. In this paper, we illustrate how to practically combine the generality and learning potential of off-policy learning with the flexibility in action selection given by actor-critic methods. We derive an incremental, linear time and space complexity algorithm that includes eligibility traces, prove convergence under assumptions similar to previous off-policy algorithms, and empirically show better or comparable performance to existing algorithms on standard reinforcement-learning benchmark problems.

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