arXiv subjects

Dale Schuurmans

Publications and source records attributed to Dale Schuurmans.

At least 73 records · Page 4Linked to original sources

arXiv2022

Making Linear MDPs Practical via Contrastive Representation Learning

It is common to address the curse of dimensionality in Markov decision processes (MDPs) by exploiting low-rank representations. This motivates much of the recent theoretical study on linear MDPs. However, most approaches require a given representation under unrealistic assumptions about the normalization of the decomposition or introduce unresolved computational challenges in practice. Instead, we consider an alternative definition of linear MDPs that automatically ensures normalization while allowing efficient representation learning via contrastive estimation. The framework also admits confidence-adjusted index algorithms, enabling an efficient and principled approach to incorporating optimism or pessimism in the face of uncertainty. To the best of our knowledge, this provides the first practical representation learning method for linear MDPs that achieves both strong theoretical guarantees and empirical performance. Theoretically, we prove that the proposed algorithm is sample efficient in both the online and offline settings. Empirically, we demonstrate superior performance over existing state-of-the-art model-based and model-free algorithms on several benchmarks.

cs.LG↗

arXiv2022

TEMPERA: Test-Time Prompting via Reinforcement Learning

Careful prompt design is critical to the use of large language models in zero-shot or few-shot learning. As a consequence, there is a growing interest in automated methods to design optimal prompts. In this work, we propose Test-time Prompt Editing using Reinforcement learning (TEMPERA). In contrast to prior prompt generation methods, TEMPERA can efficiently leverage prior knowledge, is adaptive to different queries and provides an interpretable prompt for every query. To achieve this, we design a novel action space that allows flexible editing of the initial prompts covering a wide set of commonly-used components like instructions, few-shot exemplars, and verbalizers. The proposed method achieves significant gains compared with recent SoTA approaches like prompt tuning, AutoPrompt, and RLPrompt, across a variety of tasks including sentiment analysis, topic classification, natural language inference, and reading comprehension. Our method achieves 5.33x on average improvement in sample efficiency when compared to the traditional fine-tuning methods.

cs.CL↗

arXiv2022

On the Global Convergence Rates of Decentralized Softmax Gradient Play in Markov Potential Games

Softmax policy gradient is a popular algorithm for policy optimization in single-agent reinforcement learning, particularly since projection is not needed for each gradient update. However, in multi-agent systems, the lack of central coordination introduces significant additional difficulties in the convergence analysis. Even for a stochastic game with identical interest, there can be multiple Nash Equilibria (NEs), which disables proof techniques that rely on the existence of a unique global optimum. Moreover, the softmax parameterization introduces non-NE policies with zero gradient, making it difficult for gradient-based algorithms in seeking NEs. In this paper, we study the finite time convergence of decentralized softmax gradient play in a special form of game, Markov Potential Games (MPGs), which includes the identical interest game as a special case. We investigate both gradient play and natural gradient play, with and without $\log$-barrier regularization. The established convergence rates for the unregularized cases contain a trajectory-dependent constant that can be arbitrarily large, whereas the $\log$-barrier regularization overcomes this drawback, with the cost of slightly worse dependence on other factors such as the action set size. An empirical study on an identical interest matrix game confirms the theoretical findings.

math.OC↗

arXiv2022

Dichotomy of Control: Separating What You Can Control from What You Cannot

Future- or return-conditioned supervised learning is an emerging paradigm for offline reinforcement learning (RL), where the future outcome (i.e., return) associated with an observed action sequence is used as input to a policy trained to imitate those same actions. While return-conditioning is at the heart of popular algorithms such as decision transformer (DT), these methods tend to perform poorly in highly stochastic environments, where an occasional high return can arise from randomness in the environment rather than the actions themselves. Such situations can lead to a learned policy that is inconsistent with its conditioning inputs; i.e., using the policy to act in the environment, when conditioning on a specific desired return, leads to a distribution of real returns that is wildly different than desired. In this work, we propose the dichotomy of control (DoC), a future-conditioned supervised learning framework that separates mechanisms within a policy's control (actions) from those beyond a policy's control (environment stochasticity). We achieve this separation by conditioning the policy on a latent variable representation of the future, and designing a mutual information constraint that removes any information from the latent variable associated with randomness in the environment. Theoretically, we show that DoC yields policies that are consistent with their conditioning inputs, ensuring that conditioning a learned policy on a desired high-return future outcome will correctly induce high-return behavior. Empirically, we show that DoC is able to achieve significantly better performance than DT on environments that have highly stochastic rewards and transition

cs.LG↗

arXiv2022

Multimodal Masked Autoencoders Learn Transferable Representations

Building scalable models to learn from diverse, multimodal data remains an open challenge. For vision-language data, the dominant approaches are based on contrastive learning objectives that train a separate encoder for each modality. While effective, contrastive learning approaches introduce sampling bias depending on the data augmentations used, which can degrade performance on downstream tasks. Moreover, these methods are limited to paired image-text data, and cannot leverage widely-available unpaired data. In this paper, we investigate whether a large multimodal model trained purely via masked token prediction, without using modality-specific encoders or contrastive learning, can learn transferable representations for downstream tasks. We propose a simple and scalable network architecture, the Multimodal Masked Autoencoder (M3AE), which learns a unified encoder for both vision and language data via masked token prediction. We provide an empirical study of M3AE trained on a large-scale image-text dataset, and find that M3AE is able to learn generalizable representations that transfer well to downstream tasks. Surprisingly, we find that M3AE benefits from a higher text mask ratio (50-90%), in contrast to BERT whose standard masking ratio is 15%, due to the joint training of two data modalities. We also provide qualitative analysis showing that the learned representation incorporates meaningful information from both image and language. Lastly, we demonstrate the scalability of M3AE with larger model size and training time, and its flexibility to train on both paired image-text data as well as unpaired data.

cs.CV↗

arXiv2022

Optimal Scaling for Locally Balanced Proposals in Discrete Spaces

Optimal scaling has been well studied for Metropolis-Hastings (M-H) algorithms in continuous spaces, but a similar understanding has been lacking in discrete spaces. Recently, a family of locally balanced proposals (LBP) for discrete spaces has been proved to be asymptotically optimal, but the question of optimal scaling has remained open. In this paper, we establish, for the first time, that the efficiency of M-H in discrete spaces can also be characterized by an asymptotic acceptance rate that is independent of the target distribution. Moreover, we verify, both theoretically and empirically, that the optimal acceptance rates for LBP and random walk Metropolis (RWM) are $0.574$ and $0.234$ respectively. These results also help establish that LBP is asymptotically $O(N^\frac{2}{3})$ more efficient than RWM with respect to model dimension $N$. Knowledge of the optimal acceptance rate allows one to automatically tune the neighborhood size of a proposal distribution in a discrete space, directly analogous to step-size control in continuous spaces. We demonstrate empirically that such adaptive M-H sampling can robustly improve sampling in a variety of target distributions in discrete spaces, including training deep energy based models.

cs.LG↗

arXiv2022

Rationale-Augmented Ensembles in Language Models

Recent research has shown that rationales, or step-by-step chains of thought, can be used to improve performance in multi-step reasoning tasks. We reconsider rationale-augmented prompting for few-shot in-context learning, where (input -> output) prompts are expanded to (input, rationale -> output) prompts. For rationale-augmented prompting we demonstrate how existing approaches, which rely on manual prompt engineering, are subject to sub-optimal rationales that may harm performance. To mitigate this brittleness, we propose a unified framework of rationale-augmented ensembles, where we identify rationale sampling in the output space as the key component to robustly improve performance. This framework is general and can easily be extended to common natural language processing tasks, even those that do not traditionally leverage intermediate steps, such as question answering, word sense disambiguation, and sentiment analysis. We demonstrate that rationale-augmented ensembles achieve more accurate and interpretable results than existing prompting approaches--including standard prompting without rationales and rationale-based chain-of-thought prompting--while simultaneously improving interpretability of model predictions through the associated rationales.

cs.CL↗

arXiv2022

A Parametric Class of Approximate Gradient Updates for Policy Optimization

Approaches to policy optimization have been motivated from diverse principles, based on how the parametric model is interpreted (e.g. value versus policy representation) or how the learning objective is formulated, yet they share a common goal of maximizing expected return. To better capture the commonalities and identify key differences between policy optimization methods, we develop a unified perspective that re-expresses the underlying updates in terms of a limited choice of gradient form and scaling function. In particular, we identify a parameterized space of approximate gradient updates for policy optimization that is highly structured, yet covers both classical and recent examples, including PPO. As a result, we obtain novel yet well motivated updates that generalize existing algorithms in a way that can deliver benefits both in terms of convergence speed and final result quality. An experimental investigation demonstrates that the additional degrees of freedom provided in the parameterized family of updates can be leveraged to obtain non-trivial improvements both in synthetic domains and on popular deep RL benchmarks.

cs.LG↗

arXiv2022

On the Global Convergence Rates of Softmax Policy Gradient Methods

We make three contributions toward better understanding policy gradient methods in the tabular setting. First, we show that with the true gradient, policy gradient with a softmax parametrization converges at a $O(1/t)$ rate, with constants depending on the problem and initialization. This result significantly expands the recent asymptotic convergence results. The analysis relies on two findings: that the softmax policy gradient satisfies a Łojasiewicz inequality, and the minimum probability of an optimal action during optimization can be bounded in terms of its initial value. Second, we analyze entropy regularized policy gradient and show that it enjoys a significantly faster linear convergence rate $O(e^{-c \cdot t})$ toward softmax optimal policy $(c > 0)$. This result resolves an open question in the recent literature. Finally, combining the above two results and additional new $Ω(1/t)$ lower bound results, we explain how entropy regularization improves policy optimization, even with the true gradient, from the perspective of convergence rate. The separation of rates is further explained using the notion of non-uniform Łojasiewicz degree. These results provide a theoretical understanding of the impact of entropy and corroborate existing empirical studies.

cs.LG↗

arXiv2022

Leveraging Non-uniformity in First-order Non-convex Optimization

Classical global convergence results for first-order methods rely on uniform smoothness and the Łojasiewicz inequality. Motivated by properties of objective functions that arise in machine learning, we propose a non-uniform refinement of these notions, leading to \emph{Non-uniform Smoothness} (NS) and \emph{Non-uniform Łojasiewicz inequality} (NŁ). The new definitions inspire new geometry-aware first-order methods that are able to converge to global optimality faster than the classical $Ω(1/t^2)$ lower bounds. To illustrate the power of these geometry-aware methods and their corresponding non-uniform analysis, we consider two important problems in machine learning: policy gradient optimization in reinforcement learning (PG), and generalized linear model training in supervised learning (GLM). For PG, we find that normalizing the gradient ascent method can accelerate convergence to $O(e^{-t})$ while incurring less overhead than existing algorithms. For GLM, we show that geometry-aware normalized gradient descent can also achieve a linear convergence rate, which significantly improves the best known results. We additionally show that the proposed geometry-aware descent methods escape landscape plateaus faster than standard gradient descent. Experimental results are used to illustrate and complement the theoretical findings.

cs.LG↗

arXiv2022

Chain of Thought Imitation with Procedure Cloning

Imitation learning aims to extract high-performance policies from logged demonstrations of expert behavior. It is common to frame imitation learning as a supervised learning problem in which one fits a function approximator to the input-output mapping exhibited by the logged demonstrations (input observations to output actions). While the framing of imitation learning as a supervised input-output learning problem allows for applicability in a wide variety of settings, it is also an overly simplistic view of the problem in situations where the expert demonstrations provide much richer insight into expert behavior. For example, applications such as path navigation, robot manipulation, and strategy games acquire expert demonstrations via planning, search, or some other multi-step algorithm, revealing not just the output action to be imitated but also the procedure for how to determine this action. While these intermediate computations may use tools not available to the agent during inference (e.g., environment simulators), they are nevertheless informative as a way to explain an expert's mapping of state to actions. To properly leverage expert procedure information without relying on the privileged tools the expert may have used to perform the procedure, we propose procedure cloning, which applies supervised sequence prediction to imitate the series of expert computations. This way, procedure cloning learns not only what to do (i.e., the output action), but how and why to do it (i.e., the procedure). Through empirical analysis on navigation, simulated robotic manipulation, and game-playing environments, we show that imitating the intermediate computations of an expert's behavior enables procedure cloning to learn policies exhibiting significant generalization to unseen environment configurations, including those configurations for which running the expert's procedure directly is infeasible.

cs.LG↗

arXiv2021

Neural Stochastic Dual Dynamic Programming

Stochastic dual dynamic programming (SDDP) is a state-of-the-art method for solving multi-stage stochastic optimization, widely used for modeling real-world process optimization tasks. Unfortunately, SDDP has a worst-case complexity that scales exponentially in the number of decision variables, which severely limits applicability to only low dimensional problems. To overcome this limitation, we extend SDDP by introducing a trainable neural model that learns to map problem instances to a piece-wise linear value function within intrinsic low-dimension space, which is architected specifically to interact with a base SDDP solver, so that can accelerate optimization performance on new instances. The proposed Neural Stochastic Dual Dynamic Programming ($ν$-SDDP) continually self-improves by solving successive problems. An empirical investigation demonstrates that $ν$-SDDP can significantly reduce problem solving cost without sacrificing solution quality over competitors such as SDDP and reinforcement learning algorithms, across a range of synthetic and real-world process optimization problems.

cs.LG↗

arXiv2021

SMORE: Knowledge Graph Completion and Multi-hop Reasoning in Massive Knowledge Graphs

Knowledge graphs (KGs) capture knowledge in the form of head--relation--tail triples and are a crucial component in many AI systems. There are two important reasoning tasks on KGs: (1) single-hop knowledge graph completion, which involves predicting individual links in the KG; and (2), multi-hop reasoning, where the goal is to predict which KG entities satisfy a given logical query. Embedding-based methods solve both tasks by first computing an embedding for each entity and relation, then using them to form predictions. However, existing scalable KG embedding frameworks only support single-hop knowledge graph completion and cannot be applied to the more challenging multi-hop reasoning task. Here we present Scalable Multi-hOp REasoning (SMORE), the first general framework for both single-hop and multi-hop reasoning in KGs. Using a single machine SMORE can perform multi-hop reasoning in Freebase KG (86M entities, 338M edges), which is 1,500x larger than previously considered KGs. The key to SMORE's runtime performance is a novel bidirectional rejection sampling that achieves a square root reduction of the complexity of online training data generation. Furthermore, SMORE exploits asynchronous scheduling, overlapping CPU-based data sampling, GPU-based embedding computation, and frequent CPU--GPU IO. SMORE increases throughput (i.e., training speed) over prior multi-hop KG frameworks by 2.2x with minimal GPU memory requirements (2GB for training 400-dim embeddings on 86M-node Freebase) and achieves near linear speed-up with the number of GPUs. Moreover, on the simpler single-hop knowledge graph completion task SMORE achieves comparable or even better runtime performance to state-of-the-art frameworks on both single GPU and multi-GPU settings.

cs.LG↗

arXiv2021

Understanding the Effect of Stochasticity in Policy Optimization

We study the effect of stochasticity in on-policy policy optimization, and make the following four contributions. First, we show that the preferability of optimization methods depends critically on whether stochastic versus exact gradients are used. In particular, unlike the true gradient setting, geometric information cannot be easily exploited in the stochastic case for accelerating policy optimization without detrimental consequences or impractical assumptions. Second, to explain these findings we introduce the concept of committal rate for stochastic policy optimization, and show that this can serve as a criterion for determining almost sure convergence to global optimality. Third, we show that in the absence of external oracle information, which allows an algorithm to determine the difference between optimal and sub-optimal actions given only on-policy samples, there is an inherent trade-off between exploiting geometry to accelerate convergence versus achieving optimality almost surely. That is, an uninformed algorithm either converges to a globally optimal policy with probability $1$ but at a rate no better than $O(1/t)$, or it achieves faster than $O(1/t)$ convergence but then must fail to converge to the globally optimal policy with some positive probability. Finally, we use the committal rate theory to explain why practical policy optimization methods are sensitive to random initialization, then develop an ensemble method that can be guaranteed to achieve near-optimal solutions with high probability.

cs.LG↗

arXiv2021

Combiner: Full Attention Transformer with Sparse Computation Cost

Transformers provide a class of expressive architectures that are extremely effective for sequence modeling. However, the key limitation of transformers is their quadratic memory and time complexity $\mathcal{O}(L^2)$ with respect to the sequence length in attention layers, which restricts application in extremely long sequences. Most existing approaches leverage sparsity or low-rank assumptions in the attention matrix to reduce cost, but sacrifice expressiveness. Instead, we propose Combiner, which provides full attention capability in each attention head while maintaining low computation and memory complexity. The key idea is to treat the self-attention mechanism as a conditional expectation over embeddings at each location, and approximate the conditional distribution with a structured factorization. Each location can attend to all other locations, either via direct attention, or through indirect attention to abstractions, which are again conditional expectations of embeddings from corresponding local regions. We show that most sparse attention patterns used in existing sparse transformers are able to inspire the design of such factorization for full attention, resulting in the same sub-quadratic cost ($\mathcal{O}(L\log(L))$ or $\mathcal{O}(L\sqrt{L})$). Combiner is a drop-in replacement for attention layers in existing transformers and can be easily implemented in common frameworks. An experimental evaluation on both autoregressive and bidirectional sequence tasks demonstrates the effectiveness of this approach, yielding state-of-the-art results on several image and text modeling tasks.

cs.LG↗

arXiv2021

Joint Attention for Multi-Agent Coordination and Social Learning

Joint attention - the ability to purposefully coordinate attention with another agent, and mutually attend to the same thing -- is a critical component of human social cognition. In this paper, we ask whether joint attention can be useful as a mechanism for improving multi-agent coordination and social learning. We first develop deep reinforcement learning (RL) agents with a recurrent visual attention architecture. We then train agents to minimize the difference between the attention weights that they apply to the environment at each timestep, and the attention of other agents. Our results show that this joint attention incentive improves agents' ability to solve difficult coordination tasks, by reducing the exponential cost of exploring the joint multi-agent action space. Joint attention leads to higher performance than a competitive centralized critic baseline across multiple environments. Further, we show that joint attention enhances agents' ability to learn from experts present in their environment, even when completing hard exploration tasks that do not require coordination. Taken together, these findings suggest that joint attention may be a useful inductive bias for multi-agent learning.

cs.AI↗

arXiv2021

Characterizing the Gap Between Actor-Critic and Policy Gradient

Actor-critic (AC) methods are ubiquitous in reinforcement learning. Although it is understood that AC methods are closely related to policy gradient (PG), their precise connection has not been fully characterized previously. In this paper, we explain the gap between AC and PG methods by identifying the exact adjustment to the AC objective/gradient that recovers the true policy gradient of the cumulative reward objective (PG). Furthermore, by viewing the AC method as a two-player Stackelberg game between the actor and critic, we show that the Stackelberg policy gradient can be recovered as a special case of our more general analysis. Based on these results, we develop practical algorithms, Residual Actor-Critic and Stackelberg Actor-Critic, for estimating the correction between AC and PG and use these to modify the standard AC algorithm. Experiments on popular tabular and continuous environments show the proposed corrections can improve both the sample efficiency and final performance of existing AC methods.

cs.AI↗

arXiv2021

On the Optimality of Batch Policy Optimization Algorithms

Batch policy optimization considers leveraging existing data for policy construction before interacting with an environment. Although interest in this problem has grown significantly in recent years, its theoretical foundations remain under-developed. To advance the understanding of this problem, we provide three results that characterize the limits and possibilities of batch policy optimization in the finite-armed stochastic bandit setting. First, we introduce a class of confidence-adjusted index algorithms that unifies optimistic and pessimistic principles in a common framework, which enables a general analysis. For this family, we show that any confidence-adjusted index algorithm is minimax optimal, whether it be optimistic, pessimistic or neutral. Our analysis reveals that instance-dependent optimality, commonly used to establish optimality of on-line stochastic bandit algorithms, cannot be achieved by any algorithm in the batch setting. In particular, for any algorithm that performs optimally in some environment, there exists another environment where the same algorithm suffers arbitrarily larger regret. Therefore, to establish a framework for distinguishing algorithms, we introduce a new weighted-minimax criterion that considers the inherent difficulty of optimal value prediction. We demonstrate how this criterion can be used to justify commonly used pessimistic principles for batch policy optimization.

cs.LG↗