arXiv subjects

Martha White

Publications and source records attributed to Martha White.

At least 73 records · Page 4Linked to original sources

arXiv2022

A Temporal-Difference Approach to Policy Gradient Estimation

The policy gradient theorem (Sutton et al., 2000) prescribes the usage of a cumulative discounted state distribution under the target policy to approximate the gradient. Most algorithms based on this theorem, in practice, break this assumption, introducing a distribution shift that can cause the convergence to poor solutions. In this paper, we propose a new approach of reconstructing the policy gradient from the start state without requiring a particular sampling strategy. The policy gradient calculation in this form can be simplified in terms of a gradient critic, which can be recursively estimated due to a new Bellman equation of gradients. By using temporal-difference updates of the gradient critic from an off-policy data stream, we develop the first estimator that sidesteps the distribution shift issue in a model-free way. We prove that, under certain realizability conditions, our estimator is unbiased regardless of the sampling strategy. We empirically show that our technique achieves a superior bias-variance trade-off and performance in presence of off-policy samples.

cs.LG↗

arXiv2022

Understanding and Mitigating the Limitations of Prioritized Experience Replay

Prioritized Experience Replay (ER) has been empirically shown to improve sample efficiency across many domains and attracted great attention; however, there is little theoretical understanding of why such prioritized sampling helps and its limitations. In this work, we take a deep look at the prioritized ER. In a supervised learning setting, we show the equivalence between the error-based prioritized sampling method for mean squared error and uniform sampling for cubic power loss. We then provide theoretical insight into why it improves convergence rate upon uniform sampling during early learning. Based on the insight, we further point out two limitations of the prioritized ER method: 1) outdated priorities and 2) insufficient coverage of the sample space. To mitigate the limitations, we propose our model-based stochastic gradient Langevin dynamics sampling method. We show that our method does provide states distributed close to an ideal prioritized sampling distribution estimated by the brute-force method, which does not suffer from the two limitations. We conduct experiments on both discrete and continuous control problems to show our approach's efficacy and examine the practical implication of our method in an autonomous driving application.

cs.AI↗

arXiv2022

No More Pesky Hyperparameters: Offline Hyperparameter Tuning for RL

The performance of reinforcement learning (RL) agents is sensitive to the choice of hyperparameters. In real-world settings like robotics or industrial control systems, however, testing different hyperparameter configurations directly on the environment can be financially prohibitive, dangerous, or time consuming. We propose a new approach to tune hyperparameters from offline logs of data, to fully specify the hyperparameters for an RL agent that learns online in the real world. The approach is conceptually simple: we first learn a model of the environment from the offline data, which we call a calibration model, and then simulate learning in the calibration model to identify promising hyperparameters. We identify several criteria to make this strategy effective, and develop an approach that satisfies these criteria. We empirically investigate the method in a variety of settings to identify when it is effective and when it fails.

cs.LG↗

arXiv2022

Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences

Approximate Policy Iteration (API) algorithms alternate between (approximate) policy evaluation and (approximate) greedification. Many different approaches have been explored for approximate policy evaluation, but less is understood about approximate greedification and what choices guarantee policy improvement. In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization. We show that the reverse KL has stronger policy improvement guarantees, but that reducing the forward KL can result in a worse policy. We also demonstrate, however, that a large enough reduction of the forward KL can induce improvement under additional assumptions. Empirically, we show on simple continuous-action environments that the forward KL can induce more exploration, but at the cost of a more suboptimal policy. No significant differences were observed in the discrete-action setting or on a suite of benchmark problems. Throughout, we highlight that many policy gradient methods can be seen as an instance of API, with either the forward or reverse KL for the policy update, and discuss next steps for understanding and improving our policy optimization algorithms.

cs.LG↗

arXiv2022

Resonance in Weight Space: Covariate Shift Can Drive Divergence of SGD with Momentum

Most convergence guarantees for stochastic gradient descent with momentum (SGDm) rely on iid sampling. Yet, SGDm is often used outside this regime, in settings with temporally correlated input samples such as continual learning and reinforcement learning. Existing work has shown that SGDm with a decaying step-size can converge under Markovian temporal correlation. In this work, we show that SGDm under covariate shift with a fixed step-size can be unstable and diverge. In particular, we show SGDm under covariate shift is a parametric oscillator, and so can suffer from a phenomenon known as resonance. We approximate the learning system as a time varying system of ordinary differential equations, and leverage existing theory to characterize the system's divergence/convergence as resonant/nonresonant modes. The theoretical result is limited to the linear setting with periodic covariate shift, so we empirically supplement this result to show that resonance phenomena persist even under non-periodic covariate shift, nonlinear dynamics with neural networks, and optimizers other than SGDm.

cs.LG↗

arXiv2022

An Alternate Policy Gradient Estimator for Softmax Policies

Policy gradient (PG) estimators are ineffective in dealing with softmax policies that are sub-optimally saturated, which refers to the situation when the policy concentrates its probability mass on sub-optimal actions. Sub-optimal policy saturation may arise from bad policy initialization or sudden changes in the environment that occur after the policy has already converged. Current softmax PG estimators require a large number of updates to overcome policy saturation, which causes low sample efficiency and poor adaptability to new situations. To mitigate this problem, we propose a novel PG estimator for softmax policies that utilizes the bias in the critic estimate and the noise present in the reward signal to escape the saturated regions of the policy parameter space. Our theoretical analysis and experiments, conducted on bandits and various reinforcement learning environments, show that this new estimator is significantly more robust to policy saturation.

cs.LG↗

arXiv2022

Continual Auxiliary Task Learning

Learning auxiliary tasks, such as multiple predictions about the world, can provide many benefits to reinforcement learning systems. A variety of off-policy learning algorithms have been developed to learn such predictions, but as yet there is little work on how to adapt the behavior to gather useful data for those off-policy predictions. In this work, we investigate a reinforcement learning system designed to learn a collection of auxiliary tasks, with a behavior policy learning to take actions to improve those auxiliary predictions. We highlight the inherent non-stationarity in this continual auxiliary task learning problem, for both prediction learners and the behavior learner. We develop an algorithm based on successor features that facilitates tracking under non-stationary rewards, and prove the separation into learning successor features and rewards provides convergence rate improvements. We conduct an in-depth study into the resulting multi-prediction learning system.

cs.LG↗

arXiv2021

Unifying task specification in reinforcement learning

Reinforcement learning tasks are typically specified as Markov decision processes. This formalism has been highly successful, though specifications often couple the dynamics of the environment and the learning objective. This lack of modularity can complicate generalization of the task specification, as well as obfuscate connections between different task settings, such as episodic and continuing. In this work, we introduce the RL task formalism, that provides a unification through simple constructs including a generalization to transition-based discounting. Through a series of examples, we demonstrate the generality and utility of this formalism. Finally, we extend standard learning constructs, including Bellman operators, and extend some seminal theoretical results, including approximation errors bounds. Overall, we provide a well-understood and sound formalism on which to build theoretical results and simplify algorithm use and development.

cs.AI↗

arXiv2021

Maxmin Q-learning: Controlling the Estimation Bias of Q-learning

Q-learning suffers from overestimation bias, because it approximates the maximum action value using the maximum estimated action value. Algorithms have been proposed to reduce overestimation bias, but we lack an understanding of how bias interacts with performance, and the extent to which existing algorithms mitigate bias. In this paper, we 1) highlight that the effect of overestimation bias on learning efficiency is environment-dependent; 2) propose a generalization of Q-learning, called \emph{Maxmin Q-learning}, which provides a parameter to flexibly control bias; 3) show theoretically that there exists a parameter choice for Maxmin Q-learning that leads to unbiased estimation with a lower approximation variance than Q-learning; and 4) prove the convergence of our algorithm in the tabular case, as well as convergence of several previous Q-learning variants, using a novel Generalized Q-learning framework. We empirically verify that our algorithm better controls estimation bias in toy environments, and that it achieves superior performance on several benchmark problems.

cs.LG↗

arXiv2021

Predictive Representation Learning for Language Modeling

To effectively perform the task of next-word prediction, long short-term memory networks (LSTMs) must keep track of many types of information. Some information is directly related to the next word's identity, but some is more secondary (e.g. discourse-level features or features of downstream words). Correlates of secondary information appear in LSTM representations even though they are not part of an \emph{explicitly} supervised prediction task. In contrast, in reinforcement learning (RL), techniques that explicitly supervise representations to predict secondary information have been shown to be beneficial. Inspired by that success, we propose Predictive Representation Learning (PRL), which explicitly constrains LSTMs to encode specific predictions, like those that might need to be learned implicitly. We show that PRL 1) significantly improves two strong language modeling methods, 2) converges more quickly, and 3) performs better when data is limited. Our work shows that explicitly encoding a simple predictive task facilitates the search for a more effective language model.

cs.CL↗

arXiv2021

Context-Dependent Upper-Confidence Bounds for Directed Exploration

Directed exploration strategies for reinforcement learning are critical for learning an optimal policy in a minimal number of interactions with the environment. Many algorithms use optimism to direct exploration, either through visitation estimates or upper confidence bounds, as opposed to data-inefficient strategies like ε-greedy that use random, undirected exploration. Most data-efficient exploration methods require significant computation, typically relying on a learned model to guide exploration. Least-squares methods have the potential to provide some of the data-efficiency benefits of model-based approaches -- because they summarize past interactions -- with the computation closer to that of model-free approaches. In this work, we provide a novel, computationally efficient, incremental exploration strategy, leveraging this property of least-squares temporal difference learning (LSTD). We derive upper confidence bounds on the action-values learned by LSTD, with context-dependent (or state-dependent) noise variance. Such context-dependent noise focuses exploration on a subset of variable states, and allows for reduced exploration in other states. We empirically demonstrate that our algorithm can converge more quickly than other incremental exploration strategies using confidence estimates on action-values.

cs.LG↗

arXiv2021

Fuzzy Tiling Activations: A Simple Approach to Learning Sparse Representations Online

Recent work has shown that sparse representations -- where only a small percentage of units are active -- can significantly reduce interference. Those works, however, relied on relatively complex regularization or meta-learning approaches, that have only been used offline in a pre-training phase. In this work, we pursue a direction that achieves sparsity by design, rather than by learning. Specifically, we design an activation function that produces sparse representations deterministically by construction, and so is more amenable to online training. The idea relies on the simple approach of binning, but overcomes the two key limitations of binning: zero gradients for the flat regions almost everywhere, and lost precision -- reduced discrimination -- due to coarse aggregation. We introduce a Fuzzy Tiling Activation (FTA) that provides non-negligible gradients and produces overlap between bins that improves discrimination. We first show that FTA is robust under covariate shift in a synthetic online supervised learning problem, where we can vary the level of correlation and drift. Then we move to the deep reinforcement learning setting and investigate both value-based and policy gradient algorithms that use neural networks with FTAs, in classic discrete control and Mujoco continuous control environments. We show that algorithms equipped with FTAs are able to learn a stable policy faster without needing target networks on most domains.

cs.LG↗

arXiv2021

Scalable Online Recurrent Learning Using Columnar Neural Networks

Structural credit assignment for recurrent learning is challenging. An algorithm called RTRL can compute gradients for recurrent networks online but is computationally intractable for large networks. Alternatives, such as BPTT, are not online. In this work, we propose a credit-assignment algorithm -- \algoname{} -- that approximates the gradients for recurrent learning in real-time using $O(n)$ operations and memory per-step. Our method builds on the idea that for modular recurrent networks, composed of columns with scalar states, it is sufficient for a parameter to only track its influence on the state of its column. We empirically show that as long as connections between columns are sparse, our method approximates the true gradient well. In the special case when there are no connections between columns, the $O(n)$ gradient estimate is exact. We demonstrate the utility of the approach for both recurrent state learning and meta-learning by comparing the estimated gradient to the true gradient on a synthetic test-bed.

cs.LG↗

arXiv2021

Selective Dyna-style Planning Under Limited Model Capacity

In model-based reinforcement learning, planning with an imperfect model of the environment has the potential to harm learning progress. But even when a model is imperfect, it may still contain information that is useful for planning. In this paper, we investigate the idea of using an imperfect model selectively. The agent should plan in parts of the state space where the model would be helpful but refrain from using the model where it would be harmful. An effective selective planning mechanism requires estimating predictive uncertainty, which arises out of aleatoric uncertainty, parameter uncertainty, and model inadequacy, among other sources. Prior work has focused on parameter uncertainty for selective planning. In this work, we emphasize the importance of model inadequacy. We show that heteroscedastic regression can signal predictive uncertainty arising from model inadequacy that is complementary to that which is detected by methods designed for parameter uncertainty, indicating that considering both parameter uncertainty and model inadequacy may be a more promising direction for effective selective planning than either in isolation.

cs.LG↗

arXiv2021

General Value Function Networks

State construction is important for learning in partially observable environments. A general purpose strategy for state construction is to learn the state update using a Recurrent Neural Network (RNN), which updates the internal state using the current internal state and the most recent observation. This internal state provides a summary of the observed sequence, to facilitate accurate predictions and decision-making. At the same time, specifying and training RNNs is notoriously tricky, particularly as the common strategy to approximate gradients back in time, called truncated Back-prop Through Time (BPTT), can be sensitive to the truncation window. Further, domain-expertise--which can usually help constrain the function class and so improve trainability--can be difficult to incorporate into complex recurrent units used within RNNs. In this work, we explore how to use multi-step predictions to constrain the RNN and incorporate prior knowledge. In particular, we revisit the idea of using predictions to construct state and ask: does constraining (parts of) the state to consist of predictions about the future improve RNN trainability? We formulate a novel RNN architecture, called a General Value Function Network (GVFN), where each internal state component corresponds to a prediction about the future represented as a value function. We first provide an objective for optimizing GVFNs, and derive several algorithms to optimize this objective. We then show that GVFNs are more robust to the truncation level, in many cases only requiring one-step gradient updates.

cs.LG↗

arXiv2020

Towards Safe Policy Improvement for Non-Stationary MDPs

Many real-world sequential decision-making problems involve critical systems with financial risks and human-life risks. While several works in the past have proposed methods that are safe for deployment, they assume that the underlying problem is stationary. However, many real-world problems of interest exhibit non-stationarity, and when stakes are high, the cost associated with a false stationarity assumption may be unacceptable. We take the first steps towards ensuring safety, with high confidence, for smoothly-varying non-stationary decision problems. Our proposed method extends a type of safe algorithm, called a Seldonian algorithm, through a synthesis of model-free reinforcement learning with time-series analysis. Safety is ensured using sequential hypothesis testing of a policy's forecasted performance, and confidence intervals are obtained using wild bootstrap.

cs.LG↗

arXiv2020

Perspectives on Sim2Real Transfer for Robotics: A Summary of the R:SS 2020 Workshop

This report presents the debates, posters, and discussions of the Sim2Real workshop held in conjunction with the 2020 edition of the "Robotics: Science and System" conference. Twelve leaders of the field took competing debate positions on the definition, viability, and importance of transferring skills from simulation to the real world in the context of robotics problems. The debaters also joined a large panel discussion, answering audience questions and outlining the future of Sim2Real in robotics. Furthermore, we invited extended abstracts to this workshop which are summarized in this report. Based on the workshop, this report concludes with directions for practitioners exploiting this technology and for researchers further exploring open problems in this area.

cs.RO↗

arXiv2020

An implicit function learning approach for parametric modal regression

For multi-valued functions---such as when the conditional distribution on targets given the inputs is multi-modal---standard regression approaches are not always desirable because they provide the conditional mean. Modal regression algorithms address this issue by instead finding the conditional mode(s). Most, however, are nonparametric approaches and so can be difficult to scale. Further, parametric approximators, like neural networks, facilitate learning complex relationships between inputs and targets. In this work, we propose a parametric modal regression algorithm. We use the implicit function theorem to develop an objective, for learning a joint function over inputs and targets. We empirically demonstrate on several synthetic problems that our method (i) can learn multi-valued functions and produce the conditional modes, (ii) scales well to high-dimensional inputs, and (iii) can even be more effective for certain uni-modal problems, particularly for high-frequency functions. We demonstrate that our method is competitive in a real-world modal regression problem and two regular regression datasets.

stat.ML↗