A central issue lying at the heart of online reinforcement learning (RL) is data efficiency. While a number of recent works achieved asymptotically minimal regret in online RL, the optimality of these results is only guaranteed in a ``large-sample'' regime, imposing enormous burn-in cost in order for their algorithms to operate optimally. How to achieve minimax-optimal regret without incurring any burn-in cost has been an open problem in RL theory. We settle this problem for the context of finite-horizon inhomogeneous Markov decision processes. Specifically, we prove that a modified version of Monotonic Value Propagation (MVP), a model-based algorithm proposed by \cite{zhang2020reinforcement}, achieves a regret on the order of (modulo log factors) \begin{equation*} \min\big\{ \sqrt{SAH^3K}, \,HK \big\}, \end{equation*} where $S$ is the number of states, $A$ is the number of actions, $H$ is the planning horizon, and $K$ is the total number of episodes. This regret matches the minimax lower bound for the entire range of sample size $K\geq 1$, essentially eliminating any burn-in requirement. It also translates to a PAC sample complexity (i.e., the number of episodes needed to yield $\varepsilon$-accuracy) of $\frac{SAH^3}{\varepsilon^2}$ up to log factor, which is minimax-optimal for the full $\varepsilon$-range. Further, we extend our theory to unveil the influences of problem-dependent quantities like the optimal value/cost and certain variances. The key technical innovation lies in the development of a new regret decomposition strategy and a novel analysis paradigm to decouple complicated statistical dependency -- a long-standing challenge facing the analysis of online RL in the sample-hungry regime.
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We present a novel approach to address the challenge of generalization in offline reinforcement learning (RL), where the agent learns from a fixed dataset without any additional interaction with the environment. Specifically, we aim to improve the agent's ability to generalize to out-of-distribution goals. To achieve this, we propose to learn a dynamics model and check if it is equivariant with respect to a fixed type of transformation, namely translations in the state space. We then use an entropy regularizer to increase the equivariant set and augment the dataset with the resulting transformed samples. Finally, we learn a new policy offline based on the augmented dataset, with an off-the-shelf offline RL algorithm. Our experimental results demonstrate that our approach can greatly improve the test performance of the policy on the considered environments.
The travelling salesman problem (TSP) is one of the well-studied NP-hard problems in the literature. The state-of-the art inexact TSP solvers are the Lin-Kernighan-Helsgaun (LKH) heuristic and Edge Assembly crossover (EAX). A recent study suggests that EAX with restart mechanisms perform well on a wide range of TSP instances. However, this study is limited to 2,000 city problems. We study for problems ranging from 2,000 to 85,900. We see that the performance of the solver varies with the type of the problem. However, combining these solvers in an ensemble setup, we are able to outperform the individual solver's performance. We see the ensemble setup as an efficient way to make use of the abundance of compute resources. In addition to EAX and LKH, we use several versions of the hybrid of EAX and Mixing Genetic Algorithm (MGA). A hybrid of MGA and EAX is known to solve some hard problems. We see that the ensemble of the hybrid version outperforms the state-of-the-art solvers on problems larger than 10,000 cities.
Reinforcement learning~(RL) is a versatile framework for learning to solve complex real-world tasks. However, influences on the learning performance of RL algorithms are often poorly understood in practice. We discuss different analysis techniques and assess their effectiveness for investigating the impact of action representations in RL. Our experiments demonstrate that the action representation can significantly influence the learning performance on popular RL benchmark tasks. The analysis results indicate that some of the performance differences can be attributed to changes in the complexity of the optimization landscape. Finally, we discuss open challenges of analysis techniques for RL algorithms.
Recent work in algorithmic fairness has highlighted the challenge of defining racial categories for the purposes of anti-discrimination. These challenges are not new but have previously fallen to the state, which enacts race through government statistics, policies, and evidentiary standards in anti-discrimination law. Drawing on the history of state race-making, we examine how longstanding questions about the nature of race and discrimination appear within the algorithmic fairness literature. Through a content analysis of 60 papers published at FAccT between 2018 and 2020, we analyze how race is conceptualized and formalized in algorithmic fairness frameworks. We note that differing notions of race are adopted inconsistently, at times even within a single analysis. We also explore the institutional influences and values associated with these choices. While we find that categories used in algorithmic fairness work often echo legal frameworks, we demonstrate that values from academic computer science play an equally important role in the construction of racial categories. Finally, we examine the reasoning behind different operationalizations of race, finding that few papers explicitly describe their choices and even fewer justify them. We argue that the construction of racial categories is a value-laden process with significant social and political consequences for the project of algorithmic fairness. The widespread lack of justification around the operationalization of race reflects institutional norms that allow these political decisions to remain obscured within the backstage of knowledge production.
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.
Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.
The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.
Recent developments in image classification and natural language processing, coupled with the rapid growth in social media usage, have enabled fundamental advances in detecting breaking events around the world in real-time. Emergency response is one such area that stands to gain from these advances. By processing billions of texts and images a minute, events can be automatically detected to enable emergency response workers to better assess rapidly evolving situations and deploy resources accordingly. To date, most event detection techniques in this area have focused on image-only or text-only approaches, limiting detection performance and impacting the quality of information delivered to crisis response teams. In this paper, we present a new multimodal fusion method that leverages both images and texts as input. In particular, we introduce a cross-attention module that can filter uninformative and misleading components from weak modalities on a sample by sample basis. In addition, we employ a multimodal graph-based approach to stochastically transition between embeddings of different multimodal pairs during training to better regularize the learning process as well as dealing with limited training data by constructing new matched pairs from different samples. We show that our method outperforms the unimodal approaches and strong multimodal baselines by a large margin on three crisis-related tasks.
Deep neural networks (DNNs) are successful in many computer vision tasks. However, the most accurate DNNs require millions of parameters and operations, making them energy, computation and memory intensive. This impedes the deployment of large DNNs in low-power devices with limited compute resources. Recent research improves DNN models by reducing the memory requirement, energy consumption, and number of operations without significantly decreasing the accuracy. This paper surveys the progress of low-power deep learning and computer vision, specifically in regards to inference, and discusses the methods for compacting and accelerating DNN models. The techniques can be divided into four major categories: (1) parameter quantization and pruning, (2) compressed convolutional filters and matrix factorization, (3) network architecture search, and (4) knowledge distillation. We analyze the accuracy, advantages, disadvantages, and potential solutions to the problems with the techniques in each category. We also discuss new evaluation metrics as a guideline for future research.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
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