arXiv subjects

Alekh Agarwal

Publications and source records attributed to Alekh Agarwal.

At least 91 records · Page 5Linked to original sources

arXiv2017

Efficient Second Order Online Learning by Sketching

We propose Sketched Online Newton (SON), an online second order learning algorithm that enjoys substantially improved regret guarantees for ill-conditioned data. SON is an enhanced version of the Online Newton Step, which, via sketching techniques enjoys a running time linear in the dimension and sketch size. We further develop sparse forms of the sketching methods (such as Oja's rule), making the computation linear in the sparsity of features. Together, the algorithm eliminates all computational obstacles in previous second order online learning approaches.

cs.LG↗

arXiv2017

Corralling a Band of Bandit Algorithms

We study the problem of combining multiple bandit algorithms (that is, online learning algorithms with partial feedback) with the goal of creating a master algorithm that performs almost as well as the best base algorithm if it were to be run on its own. The main challenge is that when run with a master, base algorithms unavoidably receive much less feedback and it is thus critical that the master not starve a base algorithm that might perform uncompetitively initially but would eventually outperform others if given enough feedback. We address this difficulty by devising a version of Online Mirror Descent with a special mirror map together with a sophisticated learning rate scheme. We show that this approach manages to achieve a more delicate balance between exploiting and exploring base algorithms than previous works yielding superior regret bounds. Our results are applicable to many settings, such as multi-armed bandits, contextual bandits, and convex bandits. As examples, we present two main applications. The first is to create an algorithm that enjoys worst-case robustness while at the same time performing much better when the environment is relatively easy. The second is to create an algorithm that works simultaneously under different assumptions of the environment, such as different priors or different loss structures.

cs.LG↗

arXiv2017

Making Contextual Decisions with Low Technical Debt

Applications and systems are constantly faced with decisions that require picking from a set of actions based on contextual information. Reinforcement-based learning algorithms such as contextual bandits can be very effective in these settings, but applying them in practice is fraught with technical debt, and no general system exists that supports them completely. We address this and create the first general system for contextual learning, called the Decision Service. Existing systems often suffer from technical debt that arises from issues like incorrect data collection and weak debuggability, issues we systematically address through our ML methodology and system abstractions. The Decision Service enables all aspects of contextual bandit learning using four system abstractions which connect together in a loop: explore (the decision space), log, learn, and deploy. Notably, our new explore and log abstractions ensure the system produces correct, unbiased data, which our learner uses for online learning and to enable real-time safeguards, all in a fully reproducible manner. The Decision Service has a simple user interface and works with a variety of applications: we present two live production deployments for content recommendation that achieved click-through improvements of 25-30%, another with 18% revenue lift in the landing page, and ongoing applications in tech support and machine failure handling. The service makes real-time decisions and learns continuously and scalably, while significantly lowering technical debt.

cs.LG↗

arXiv2016

Contextual Decision Processes with Low Bellman Rank are PAC-Learnable

This paper studies systematic exploration for reinforcement learning with rich observations and function approximation. We introduce a new model called contextual decision processes, that unifies and generalizes most prior settings. Our first contribution is a complexity measure, the Bellman rank, that we show enables tractable learning of near-optimal behavior in these processes and is naturally small for many well-studied reinforcement learning settings. Our second contribution is a new reinforcement learning algorithm that engages in systematic exploration to learn contextual decision processes with low Bellman rank. Our algorithm provably learns near-optimal behavior with a number of samples that is polynomial in all relevant parameters but independent of the number of unique observations. The approach uses Bellman error minimization with optimistic exploration and provides new insights into efficient exploration for reinforcement learning with function approximation.

cs.LG↗

arXiv2016

Contextual Semibandits via Supervised Learning Oracles

We study an online decision making problem where on each round a learner chooses a list of items based on some side information, receives a scalar feedback value for each individual item, and a reward that is linearly related to this feedback. These problems, known as contextual semibandits, arise in crowdsourcing, recommendation, and many other domains. This paper reduces contextual semibandits to supervised learning, allowing us to leverage powerful supervised learning methods in this partial-feedback setting. Our first reduction applies when the mapping from feedback to reward is known and leads to a computationally efficient algorithm with near-optimal regret. We show that this algorithm outperforms state-of-the-art approaches on real-world learning-to-rank datasets, demonstrating the advantage of oracle-based algorithms. Our second reduction applies to the previously unstudied setting when the linear mapping from feedback to reward is unknown. Our regret guarantees are superior to prior techniques that ignore the feedback.

cs.LG↗

arXiv2016

PAC Reinforcement Learning with Rich Observations

We propose and study a new model for reinforcement learning with rich observations, generalizing contextual bandits to sequential decision making. These models require an agent to take actions based on observations (features) with the goal of achieving long-term performance competitive with a large set of policies. To avoid barriers to sample-efficient learning associated with large observation spaces and general POMDPs, we focus on problems that can be summarized by a small number of hidden states and have long-term rewards that are predictable by a reactive function class. In this setting, we design and analyze a new reinforcement learning algorithm, Least Squares Value Elimination by Exploration. We prove that the algorithm learns near optimal behavior after a number of episodes that is polynomial in all relevant parameters, logarithmic in the number of policies, and independent of the size of the observation space. Our result provides theoretical justification for reinforcement learning with function approximation.

cs.LG↗

arXiv2016

Exploratory Gradient Boosting for Reinforcement Learning in Complex Domains

High-dimensional observations and complex real-world dynamics present major challenges in reinforcement learning for both function approximation and exploration. We address both of these challenges with two complementary techniques: First, we develop a gradient-boosting style, non-parametric function approximator for learning on $Q$-function residuals. And second, we propose an exploration strategy inspired by the principles of state abstraction and information acquisition under uncertainty. We demonstrate the empirical effectiveness of these techniques, first, as a preliminary check, on two standard tasks (Blackjack and $n$-Chain), and then on two much larger and more realistic tasks with high-dimensional observation spaces. Specifically, we introduce two benchmarks built within the game Minecraft where the observations are pixel arrays of the agent's visual field. A combination of our two algorithmic techniques performs competitively on the standard reinforcement-learning tasks while consistently and substantially outperforming baselines on the two tasks with high-dimensional observation spaces. The new function approximator, exploration strategy, and evaluation benchmarks are each of independent interest in the pursuit of reinforcement-learning methods that scale to real-world domains.

cs.AI↗

arXiv2016

Efficient and Parsimonious Agnostic Active Learning

We develop a new active learning algorithm for the streaming setting satisfying three important properties: 1) It provably works for any classifier representation and classification problem including those with severe noise. 2) It is efficiently implementable with an ERM oracle. 3) It is more aggressive than all previous approaches satisfying 1 and 2. To do this we create an algorithm based on a newly defined optimization problem and analyze it. We also conduct the first experimental analysis of all efficient agnostic active learning algorithms, evaluating their strengths and weaknesses in different settings.

cs.LG↗

arXiv2015

Fast Convergence of Regularized Learning in Games

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in a game uses an algorithm from our class, their individual regret decays at $O(T^{-3/4})$, while the sum of utilities converges to an approximate optimum at $O(T^{-1})$--an improvement upon the worst case $O(T^{-1/2})$ rates. We show a black-box reduction for any algorithm in the class to achieve $\tilde{O}(T^{-1/2})$ rates against an adversary, while maintaining the faster rates against algorithms in the class. Our results extend those of [Rakhlin and Shridharan 2013] and [Daskalakis et al. 2014], who only analyzed two-player zero-sum games for specific algorithms.

cs.GT↗

arXiv2015

A Lower Bound for the Optimization of Finite Sums

This paper presents a lower bound for optimizing a finite sum of $n$ functions, where each function is $L$-smooth and the sum is $μ$-strongly convex. We show that no algorithm can reach an error $ε$ in minimizing all functions from this class in fewer than $Ω(n + \sqrt{n(κ-1)}\log(1/ε))$ iterations, where $κ=L/μ$ is a surrogate condition number. We then compare this lower bound to upper bounds for recently developed methods specializing to this setting. When the functions involved in this sum are not arbitrary, but based on i.i.d. random data, then we further contrast these complexity results with those for optimal first-order methods to directly optimize the sum. The conclusion we draw is that a lot of caution is necessary for an accurate comparison, and identify machine learning scenarios where the new methods help computationally.

stat.ML↗

arXiv2015

Learning to Search Better Than Your Teacher

Methods for learning to search for structured prediction typically imitate a reference policy, with existing theoretical guarantees demonstrating low regret compared to that reference. This is unsatisfactory in many applications where the reference policy is suboptimal and the goal of learning is to improve upon it. Can learning to search work even when the reference is poor? We provide a new learning to search algorithm, LOLS, which does well relative to the reference policy, but additionally guarantees low regret compared to deviations from the learned policy: a local-optimality guarantee. Consequently, LOLS can improve upon the reference policy, unlike previous algorithms. This enables us to develop structured contextual bandits, a partial information structured prediction setting with many potential applications.

cs.LG↗

arXiv2014

Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits

We present a new algorithm for the contextual bandit learning problem, where the learner repeatedly takes one of $K$ actions in response to the observed context, and observes the reward only for that chosen action. Our method assumes access to an oracle for solving fully supervised cost-sensitive classification problems and achieves the statistically optimal regret guarantee with only $\tilde{O}(\sqrt{KT/\log N})$ oracle calls across all $T$ rounds, where $N$ is the number of policies in the policy class we compete against. By doing so, we obtain the most practical contextual bandit learning algorithm amongst approaches that work for general policy classes. We further conduct a proof-of-concept experiment which demonstrates the excellent computational and prediction performance of (an online variant of) our algorithm relative to several baselines.

cs.LG↗

arXiv2014

Scalable Nonlinear Learning with Adaptive Polynomial Expansions

Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm is designed for extreme computational efficiency, and an extensive experimental study shows that its computation/prediction tradeoff ability compares very favorably against strong baselines.

cs.LG↗

arXiv2014

Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via $\ell_1$ minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local linear convergence for this variant of alternating minimization and establish that the basin of attraction for the global optimum (corresponding to the true dictionary and the coefficients) is $\order{1/s^2}$, where $s$ is the sparsity level in each sample and the dictionary satisfies RIP. Combined with the recent results of approximate dictionary estimation, this yields provable guarantees for exact recovery of both the dictionary elements and the coefficients, when the dictionary elements are incoherent.

cs.LG↗

arXiv2014

A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries

We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary using an efficient algorithm. Our algorithm is a clustering-style procedure, where each cluster is used to estimate a dictionary element. The resulting solution can often be further cleaned up to obtain a high accuracy estimate, and we provide one simple scenario where $\ell_1$-regularized regression can be used for such a second stage.

stat.ML↗

arXiv2013

Para-active learning

Training examples are not all equally informative. Active learning strategies leverage this observation in order to massively reduce the number of examples that need to be labeled. We leverage the same observation to build a generic strategy for parallelizing learning algorithms. This strategy is effective because the search for informative examples is highly parallelizable and because we show that its performance does not deteriorate when the sifting process relies on a slightly outdated model. Parallel active learning is particularly attractive to train nonlinear models with non-linear representations because there are few practical parallel learning algorithms for such models. We report preliminary experiments using both kernel SVMs and SGD-trained neural networks.

cs.LG↗

arXiv2013

Least Squares Revisited: Scalable Approaches for Multi-class Prediction

This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially iterative least-squares updates and very versatile both in theory and in practice. On the theoretical front, we present several variants with convergence guarantees. Owing to their effective use of second-order structure, these algorithms are substantially better than first-order methods in many practical scenarios. On the empirical side, we present a scalable stagewise variant of our approach, which achieves dramatic computational speedups over popular optimization packages such as Liblinear and Vowpal Wabbit on standard datasets (MNIST and CIFAR-10), while attaining state-of-the-art accuracies.

cs.LG↗

arXiv2013

A Reliable Effective Terascale Linear Learning System

We present a system and a set of techniques for learning linear predictors with convex losses on terascale datasets, with trillions of features, {The number of features here refers to the number of non-zero entries in the data matrix.} billions of training examples and millions of parameters in an hour using a cluster of 1000 machines. Individually none of the component techniques are new, but the careful synthesis required to obtain an efficient implementation is. The result is, up to our knowledge, the most scalable and efficient linear learning system reported in the literature (as of 2011 when our experiments were conducted). We describe and thoroughly evaluate the components of the system, showing the importance of the various design choices.

cs.LG↗