arXiv subjects

Kevin Jamieson

Publications and source records attributed to Kevin Jamieson.

At least 55 records · Page 3Linked to original sources

arXiv2023

Demonstrating Large-Scale Package Manipulation via Learned Metrics of Pick Success

Automating warehouse operations can reduce logistics overhead costs, ultimately driving down the final price for consumers, increasing the speed of delivery, and enhancing the resiliency to workforce fluctuations. The past few years have seen increased interest in automating such repeated tasks but mostly in controlled settings. Tasks such as picking objects from unstructured, cluttered piles have only recently become robust enough for large-scale deployment with minimal human intervention. This paper demonstrates a large-scale package manipulation from unstructured piles in Amazon Robotics' Robot Induction (Robin) fleet, which utilizes a pick success predictor trained on real production data. Specifically, the system was trained on over 394K picks. It is used for singulating up to 5 million packages per day and has manipulated over 200 million packages during this paper's evaluation period. The developed learned pick quality measure ranks various pick alternatives in real-time and prioritizes the most promising ones for execution. The pick success predictor aims to estimate from prior experience the success probability of a desired pick by the deployed industrial robotic arms in cluttered scenes containing deformable and rigid objects with partially known properties. It is a shallow machine learning model, which allows us to evaluate which features are most important for the prediction. An online pick ranker leverages the learned success predictor to prioritize the most promising picks for the robotic arm, which are then assessed for collision avoidance. This learned ranking process is demonstrated to overcome the limitations and outperform the performance of manually engineered and heuristic alternatives. To the best of the authors' knowledge, this paper presents the first large-scale deployment of learned pick quality estimation methods in a real production system.

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arXiv2023

Active Representation Learning for General Task Space with Applications in Robotics

Representation learning based on multi-task pretraining has become a powerful approach in many domains. In particular, task-aware representation learning aims to learn an optimal representation for a specific target task by sampling data from a set of source tasks, while task-agnostic representation learning seeks to learn a universal representation for a class of tasks. In this paper, we propose a general and versatile algorithmic and theoretic framework for \textit{active representation learning}, where the learner optimally chooses which source tasks to sample from. This framework, along with a tractable meta algorithm, allows most arbitrary target and source task spaces (from discrete to continuous), covers both task-aware and task-agnostic settings, and is compatible with deep representation learning practices. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. In the bilinear case, by leveraging the non-uniform spectrum of the task representation and the calibrated source-target relevance, we prove that the sample complexity to achieve $\varepsilon$-excess risk on target scales with $ (k^*)^2 \|v^*\|_2^2 \varepsilon^{-2}$ where $k^*$ is the effective dimension of the target and $\|v^*\|_2^2 \in (0,1]$ represents the connection between source and target space. Compared to the passive one, this can save up to $\frac{1}{d_W}$ of sample complexity, where $d_W$ is the task space dimension. Finally, we demonstrate different instantiations of our meta algorithm in synthetic datasets and robotics problems, from pendulum simulations to real-world drone flight datasets. On average, our algorithms outperform baselines by $20\%-70\%$.

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arXiv2023

Optimal Exploration for Model-Based RL in Nonlinear Systems

Learning to control unknown nonlinear dynamical systems is a fundamental problem in reinforcement learning and control theory. A commonly applied approach is to first explore the environment (exploration), learn an accurate model of it (system identification), and then compute an optimal controller with the minimum cost on this estimated system (policy optimization). While existing work has shown that it is possible to learn a uniformly good model of the system~\citep{mania2020active}, in practice, if we aim to learn a good controller with a low cost on the actual system, certain system parameters may be significantly more critical than others, and we therefore ought to focus our exploration on learning such parameters. In this work, we consider the setting of nonlinear dynamical systems and seek to formally quantify, in such settings, (a) which parameters are most relevant to learning a good controller, and (b) how we can best explore so as to minimize uncertainty in such parameters. Inspired by recent work in linear systems~\citep{wagenmaker2021task}, we show that minimizing the controller loss in nonlinear systems translates to estimating the system parameters in a particular, task-dependent metric. Motivated by this, we develop an algorithm able to efficiently explore the system to reduce uncertainty in this metric, and prove a lower bound showing that our approach learns a controller at a near-instance-optimal rate. Our algorithm relies on a general reduction from policy optimization to optimal experiment design in arbitrary systems, and may be of independent interest. We conclude with experiments demonstrating the effectiveness of our method in realistic nonlinear robotic systems.

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arXiv2023

Improved Active Multi-Task Representation Learning via Lasso

To leverage the copious amount of data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, most existing works design a source task selection strategy from a purely empirical perspective. Recently, \citet{chen2022active} gave the first active multi-task representation learning (A-MTRL) algorithm which adaptively samples from source tasks and can provably reduce the total sample complexity using the L2-regularized-target-source-relevance parameter $ν^2$. But their work is theoretically suboptimal in terms of total source sample complexity and is less practical in some real-world scenarios where sparse training source task selection is desired. In this paper, we address both issues. Specifically, we show the strict dominance of the L1-regularized-relevance-based ($ν^1$-based) strategy by giving a lower bound for the $ν^2$-based strategy. When $ν^1$ is unknown, we propose a practical algorithm that uses the LASSO program to estimate $ν^1$. Our algorithm successfully recovers the optimal result in the known case. In addition to our sample complexity results, we also characterize the potential of our $ν^1$-based strategy in sample-cost-sensitive settings. Finally, we provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method.

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arXiv2023

The Simulator: Understanding Adaptive Sampling in the Moderate-Confidence Regime

We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how difficult it is to distinguish a good sampling strategy from a bad one given the limited amount of data collected up to any given time. This change of perspective allows us to match the strength of both Fano and change-of-measure techniques, without succumbing to the limitations of either method. For concreteness, we apply our techniques to a structured multi-arm bandit problem in the fixed-confidence pure exploration setting, where we show that the constraints on the means imply a substantial gap between the moderate-confidence sample complexity, and the asymptotic sample complexity as $δ\to 0$ found in the literature. We also prove the first instance-based lower bounds for the top-k problem which incorporate the appropriate log-factors. Moreover, our lower bounds zero-in on the number of times each \emph{individual} arm needs to be pulled, uncovering new phenomena which are drowned out in the aggregate sample complexity. Our new analysis inspires a simple and near-optimal algorithm for the best-arm and top-k identification, the first {\em practical} algorithm of its kind for the latter problem which removes extraneous log factors, and outperforms the state-of-the-art in experiments.

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arXiv2023

Instance-dependent Sample Complexity Bounds for Zero-sum Matrix Games

We study the sample complexity of identifying an approximate equilibrium for two-player zero-sum $n\times 2$ matrix games. That is, in a sequence of repeated game plays, how many rounds must the two players play before reaching an approximate equilibrium (e.g., Nash)? We derive instance-dependent bounds that define an ordering over game matrices that captures the intuition that the dynamics of some games converge faster than others. Specifically, we consider a stochastic observation model such that when the two players choose actions $i$ and $j$, respectively, they both observe each other's played actions and a stochastic observation $X_{ij}$ such that $\mathbb E[ X_{ij}] = A_{ij}$. To our knowledge, our work is the first case of instance-dependent lower bounds on the number of rounds the players must play before reaching an approximate equilibrium in the sense that the number of rounds depends on the specific properties of the game matrix $A$ as well as the desired accuracy. We also prove a converse statement: there exist player strategies that achieve this lower bound.

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arXiv2022

First-Order Regret in Reinforcement Learning with Linear Function Approximation: A Robust Estimation Approach

Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making. While such bounds exist in many settings, they have proven elusive in reinforcement learning with large state spaces. In this work we address this gap, and show that it is possible to obtain regret scaling as $\widetilde{\mathcal{O}}(\sqrt{d^3 H^3 \cdot V_1^\star \cdot K} + d^{3.5}H^3\log K )$ in reinforcement learning with large state spaces, namely the linear MDP setting. Here $V_1^\star$ is the value of the optimal policy and $K$ is the number of episodes. We demonstrate that existing techniques based on least squares estimation are insufficient to obtain this result, and instead develop a novel robust self-normalized concentration bound based on the robust Catoni mean estimator, which may be of independent interest.

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arXiv2022

Instance-optimal PAC Algorithms for Contextual Bandits

In the stochastic contextual bandit setting, regret-minimizing algorithms have been extensively researched, but their instance-minimizing best-arm identification counterparts remain seldom studied. In this work, we focus on the stochastic bandit problem in the $(ε,δ)$-$\textit{PAC}$ setting: given a policy class $Π$ the goal of the learner is to return a policy $π\in Π$ whose expected reward is within $ε$ of the optimal policy with probability greater than $1-δ$. We characterize the first $\textit{instance-dependent}$ PAC sample complexity of contextual bandits through a quantity $ρ_Π$, and provide matching upper and lower bounds in terms of $ρ_Π$ for the agnostic and linear contextual best-arm identification settings. We show that no algorithm can be simultaneously minimax-optimal for regret minimization and instance-dependent PAC for best-arm identification. Our main result is a new instance-optimal and computationally efficient algorithm that relies on a polynomial number of calls to an argmax oracle.

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arXiv2022

Beyond No Regret: Instance-Dependent PAC Reinforcement Learning

The theory of reinforcement learning has focused on two fundamental problems: achieving low regret, and identifying $ε$-optimal policies. While a simple reduction allows one to apply a low-regret algorithm to obtain an $ε$-optimal policy and achieve the worst-case optimal rate, it is unknown whether low-regret algorithms can obtain the instance-optimal rate for policy identification. We show this is not possible -- there exists a fundamental tradeoff between achieving low regret and identifying an $ε$-optimal policy at the instance-optimal rate. Motivated by our negative finding, we propose a new measure of instance-dependent sample complexity for PAC tabular reinforcement learning which explicitly accounts for the attainable state visitation distributions in the underlying MDP. We then propose and analyze a novel, planning-based algorithm which attains this sample complexity -- yielding a complexity which scales with the suboptimality gaps and the "reachability" of a state. We show our algorithm is nearly minimax optimal, and on several examples that our instance-dependent sample complexity offers significant improvements over worst-case bounds.

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arXiv2022

Active Learning with Safety Constraints

Active learning methods have shown great promise in reducing the number of samples necessary for learning. As automated learning systems are adopted into real-time, real-world decision-making pipelines, it is increasingly important that such algorithms are designed with safety in mind. In this work we investigate the complexity of learning the best safe decision in interactive environments. We reduce this problem to a constrained linear bandits problem, where our goal is to find the best arm satisfying certain (unknown) safety constraints. We propose an adaptive experimental design-based algorithm, which we show efficiently trades off between the difficulty of showing an arm is unsafe vs suboptimal. To our knowledge, our results are the first on best-arm identification in linear bandits with safety constraints. In practice, we demonstrate that this approach performs well on synthetic and real world datasets.

cs.LG↗

arXiv2022

Reward-Free RL is No Harder Than Reward-Aware RL in Linear Markov Decision Processes

Reward-free reinforcement learning (RL) considers the setting where the agent does not have access to a reward function during exploration, but must propose a near-optimal policy for an arbitrary reward function revealed only after exploring. In the the tabular setting, it is well known that this is a more difficult problem than reward-aware (PAC) RL -- where the agent has access to the reward function during exploration -- with optimal sample complexities in the two settings differing by a factor of $|\mathcal{S}|$, the size of the state space. We show that this separation does not exist in the setting of linear MDPs. We first develop a computationally efficient algorithm for reward-free RL in a $d$-dimensional linear MDP with sample complexity scaling as $\widetilde{\mathcal{O}}(d^2 H^5/ε^2)$. We then show a lower bound with matching dimension-dependence of $Ω(d^2 H^2/ε^2)$, which holds for the reward-aware RL setting. To our knowledge, our approach is the first computationally efficient algorithm to achieve optimal $d$ dependence in linear MDPs, even in the single-reward PAC setting. Our algorithm relies on a novel procedure which efficiently traverses a linear MDP, collecting samples in any given ``feature direction'', and enjoys a sample complexity scaling optimally in the (linear MDP equivalent of the) maximal state visitation probability. We show that this exploration procedure can also be applied to solve the problem of obtaining ``well-conditioned'' covariates in linear MDPs.

cs.LG↗

arXiv2022

Active Multi-Task Representation Learning

To leverage the power of big data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, choosing which source tasks to include in the multi-task learning has been more art than science. In this paper, we give the first formal study on resource task sampling by leveraging the techniques from active learning. We propose an algorithm that iteratively estimates the relevance of each source task to the target task and samples from each source task based on the estimated relevance. Theoretically, we show that for the linear representation class, to achieve the same error rate, our algorithm can save up to a \textit{number of source tasks} factor in the source task sample complexity, compared with the naive uniform sampling from all source tasks. We also provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method on both linear and convolutional neural network representation classes. We believe our paper serves as an important initial step to bring techniques from active learning to representation learning.

cs.LG↗

arXiv2021

Best Arm Identification with Safety Constraints

The best arm identification problem in the multi-armed bandit setting is an excellent model of many real-world decision-making problems, yet it fails to capture the fact that in the real-world, safety constraints often must be met while learning. In this work we study the question of best-arm identification in safety-critical settings, where the goal of the agent is to find the best safe option out of many, while exploring in a way that guarantees certain, initially unknown safety constraints are met. We first analyze this problem in the setting where the reward and safety constraint takes a linear structure, and show nearly matching upper and lower bounds. We then analyze a much more general version of the problem where we only assume the reward and safety constraint can be modeled by monotonic functions, and propose an algorithm in this setting which is guaranteed to learn safely. We conclude with experimental results demonstrating the effectiveness of our approaches in scenarios such as safely identifying the best drug out of many in order to treat an illness.

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arXiv2021

Practical, Provably-Correct Interactive Learning in the Realizable Setting: The Power of True Believers

We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We begin our investigation with the observation that agnostic algorithms \emph{cannot} be minimax-optimal in the realizable setting. Hence, we design novel computationally efficient algorithms for the realizable setting that match the minimax lower bound up to logarithmic factors and are general-purpose, accommodating a wide variety of function classes including kernel methods, H{ö}lder smooth functions, and convex functions. The sample complexities of our algorithms can be quantified in terms of well-known quantities like the extended teaching dimension and haystack dimension. However, unlike algorithms based directly on those combinatorial quantities, our algorithms are computationally efficient. To achieve computational efficiency, our algorithms sample from the version space using Monte Carlo "hit-and-run" algorithms instead of maintaining the version space explicitly. Our approach has two key strengths. First, it is simple, consisting of two unifying, greedy algorithms. Second, our algorithms have the capability to seamlessly leverage prior knowledge that is often available and useful in practice. In addition to our new theoretical results, we demonstrate empirically that our algorithms are competitive with Gaussian process UCB methods.

cs.LG↗

arXiv2021

Selective Sampling for Online Best-arm Identification

This work considers the problem of selective-sampling for best-arm identification. Given a set of potential options $\mathcal{Z}\subset\mathbb{R}^d$, a learner aims to compute with probability greater than $1-δ$, $\arg\max_{z\in \mathcal{Z}} z^{\top}θ_{\ast}$ where $θ_{\ast}$ is unknown. At each time step, a potential measurement $x_t\in \mathcal{X}\subset\mathbb{R}^d$ is drawn IID and the learner can either choose to take the measurement, in which case they observe a noisy measurement of $x^{\top}θ_{\ast}$, or to abstain from taking the measurement and wait for a potentially more informative point to arrive in the stream. Hence the learner faces a fundamental trade-off between the number of labeled samples they take and when they have collected enough evidence to declare the best arm and stop sampling. The main results of this work precisely characterize this trade-off between labeled samples and stopping time and provide an algorithm that nearly-optimally achieves the minimal label complexity given a desired stopping time. In addition, we show that the optimal decision rule has a simple geometric form based on deciding whether a point is in an ellipse or not. Finally, our framework is general enough to capture binary classification improving upon previous works.

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arXiv2021

Nearly Optimal Algorithms for Level Set Estimation

The level set estimation problem seeks to find all points in a domain ${\cal X}$ where the value of an unknown function $f:{\cal X}\rightarrow \mathbb{R}$ exceeds a threshold $α$. The estimation is based on noisy function evaluations that may be acquired at sequentially and adaptively chosen locations in ${\cal X}$. The threshold value $α$ can either be \emph{explicit} and provided a priori, or \emph{implicit} and defined relative to the optimal function value, i.e. $α= (1-ε)f(x_\ast)$ for a given $ε> 0$ where $f(x_\ast)$ is the maximal function value and is unknown. In this work we provide a new approach to the level set estimation problem by relating it to recent adaptive experimental design methods for linear bandits in the Reproducing Kernel Hilbert Space (RKHS) setting. We assume that $f$ can be approximated by a function in the RKHS up to an unknown misspecification and provide novel algorithms for both the implicit and explicit cases in this setting with strong theoretical guarantees. Moreover, in the linear (kernel) setting, we show that our bounds are nearly optimal, namely, our upper bounds match existing lower bounds for threshold linear bandits. To our knowledge this work provides the first instance-dependent, non-asymptotic upper bounds on sample complexity of level-set estimation that match information theoretic lower bounds.

stat.ML↗

arXiv2021

Task-Optimal Exploration in Linear Dynamical Systems

Exploration in unknown environments is a fundamental problem in reinforcement learning and control. In this work, we study task-guided exploration and determine what precisely an agent must learn about their environment in order to complete a particular task. Formally, we study a broad class of decision-making problems in the setting of linear dynamical systems, a class that includes the linear quadratic regulator problem. We provide instance- and task-dependent lower bounds which explicitly quantify the difficulty of completing a task of interest. Motivated by our lower bound, we propose a computationally efficient experiment-design based exploration algorithm. We show that it optimally explores the environment, collecting precisely the information needed to complete the task, and provide finite-time bounds guaranteeing that it achieves the instance- and task-optimal sample complexity, up to constant factors. Through several examples of the LQR problem, we show that performing task-guided exploration provably improves on exploration schemes which do not take into account the task of interest. Along the way, we establish that certainty equivalence decision making is instance- and task-optimal, and obtain the first algorithm for the linear quadratic regulator problem which is instance-optimal. We conclude with several experiments illustrating the effectiveness of our approach in practice.

cs.LG↗

arXiv2021

Corruption Robust Active Learning

We conduct theoretical studies on streaming-based active learning for binary classification under unknown adversarial label corruptions. In this setting, every time before the learner observes a sample, the adversary decides whether to corrupt the label or not. First, we show that, in a benign corruption setting (which includes the misspecification setting as a special case), with a slight enlargement on the hypothesis elimination threshold, the classical RobustCAL framework can (surprisingly) achieve nearly the same label complexity guarantee as in the non-corrupted setting. However, this algorithm can fail in the general corruption setting. To resolve this drawback, we propose a new algorithm which is provably correct without any assumptions on the presence of corruptions. Furthermore, this algorithm enjoys the minimax label complexity in the non-corrupted setting (which is achieved by RobustCAL) and only requires $\tilde{\mathcal{O}}(C_{\mathrm{total}})$ additional labels in the corrupted setting to achieve $\mathcal{O}(\varepsilon + \frac{C_{\mathrm{total}}}{n})$, where $\varepsilon$ is the target accuracy, $C_{\mathrm{total}}$ is the total number of corruptions and $n$ is the total number of unlabeled samples.

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