In online reinforcement learning (RL), instead of employing standard structural assumptions on Markov decision processes (MDPs), using a certain coverage condition (original from offline RL) is enough to ensure sample-efficient guarantees (Xie et al. 2023). In this work, we focus on this new direction by digging more possible and general coverage conditions, and study the potential and the utility of them in efficient online RL. We identify more concepts, including the $L^p$ variant of concentrability, the density ratio realizability, and trade-off on the partial/rest coverage condition, that can be also beneficial to sample-efficient online RL, achieving improved regret bound. Furthermore, if exploratory offline data are used, under our coverage conditions, both statistically and computationally efficient guarantees can be achieved for online RL. Besides, even though the MDP structure is given, e.g., linear MDP, we elucidate that, good coverage conditions are still beneficial to obtain faster regret bound beyond $\widetilde{O}(\sqrt{T})$ and even a logarithmic order regret. These results provide a good justification for the usage of general coverage conditions in efficient online RL.
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Data heterogeneity across clients is a key challenge in federated learning. Prior works address this by either aligning client and server models or using control variates to correct client model drift. Although these methods achieve fast convergence in convex or simple non-convex problems, the performance in over-parameterized models such as deep neural networks is lacking. In this paper, we first revisit the widely used FedAvg algorithm in a deep neural network to understand how data heterogeneity influences the gradient updates across the neural network layers. We observe that while the feature extraction layers are learned efficiently by FedAvg, the substantial diversity of the final classification layers across clients impedes the performance. Motivated by this, we propose to correct model drift by variance reduction only on the final layers. We demonstrate that this significantly outperforms existing benchmarks at a similar or lower communication cost. We furthermore provide proof for the convergence rate of our algorithm.
As the real-world impact of Artificial Intelligence (AI) systems has been steadily growing, so too have these systems come under increasing scrutiny. In response, the study of AI fairness has rapidly developed into a rich field of research with links to computer science, social science, law, and philosophy. Many technical solutions for measuring and achieving AI fairness have been proposed, yet their approach has been criticized in recent years for being misleading, unrealistic and harmful. In our paper, we survey these criticisms of AI fairness and identify key limitations that are inherent to the prototypical paradigm of AI fairness. By carefully outlining the extent to which technical solutions can realistically help in achieving AI fairness, we aim to provide the background necessary to form a nuanced opinion on developments in fair AI. This delineation also provides research opportunities for non-AI solutions peripheral to AI systems in supporting fair decision processes.
Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects substantial noises and biases. These hinder the attainment of statistical guarantees and, moreover, impose computational challenges on UQ due to the need for repeated network retraining. Building upon the recent neural tangent kernel theory, we create statistically guaranteed schemes to principally \emph{quantify}, and \emph{remove}, the procedural uncertainty of over-parameterized neural networks with very low computation effort. In particular, our approach, based on what we call a procedural-noise-correcting (PNC) predictor, removes the procedural uncertainty by using only \emph{one} auxiliary network that is trained on a suitably labeled data set, instead of many retrained networks employed in deep ensembles. Moreover, by combining our PNC predictor with suitable light-computation resampling methods, we build several approaches to construct asymptotically exact-coverage confidence intervals using as low as four trained networks without additional overheads.
The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and do not make use of information about the function values; on the other hand, Bayesian optimisation is a class of promising black-box solvers with superior sample efficiency, but it has been scarcely been applied to such novel setups. To fill this gap, we propose a novel Bayesian optimisation framework that optimises over functions defined on generic, large-scale and potentially unknown graphs. Through the learning of suitable kernels on graphs, our framework has the advantage of adapting to the behaviour of the target function. The local modelling approach further guarantees the efficiency of our method. Extensive experiments on both synthetic and real-world graphs demonstrate the effectiveness of the proposed optimisation framework.
In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.
In this paper, we develop a fast and accurate pseudospectral method to approximate numerically the fractional Laplacian $(-\Delta)^{\alpha/2}$ of a function on $\mathbb{R}$ for $\alpha=1$; this case, commonly referred to as the half Laplacian, is equivalent to the Hilbert transform of the derivative of the function. The main ideas are as follows. Given a twice continuously differentiable bounded function $u\in \mathit{C}_b^2(\mathbb{R})$, we apply the change of variable $x=L\cot(s)$, with $L>0$ and $s\in[0,\pi]$, which maps $\mathbb{R}$ into $[0,\pi]$, and denote $(-\Delta)_s^{1/2}u(x(s)) \equiv (-\Delta)^{1/2}u(x)$. Therefore, by performing a Fourier series expansion of $u(x(s))$, the problem is reduced to computing $(-\Delta)_s^{1/2}e^{iks} \equiv (-\Delta)^{1/2}(x + i)^k/(1+x^2)^{k/2}$. On a previous work, we considered the case with $k$ even and $\alpha\in(0,2)$, so we focus now on the case with $k$ odd. More precisely, we express $(-\Delta)_s^{1/2}e^{iks}$ for $k$ odd in terms of the Gaussian hypergeometric function ${}_2F_1$, and also as a well-conditioned finite sum. Then, we use a fast convolution result, that enable us to compute very efficiently $\sum_{l = 0}^Ma_l(-\Delta)_s^{1/2}e^{i(2l+1)s}$, for extremely large values of $M$. This enables us to approximate $(-\Delta)_s^{1/2}u(x(s))$ in a fast and accurate way, especially when $u(x(s))$ is not periodic of period $\pi$.
Algorithms for online learning typically require one or more boundedness assumptions: that the domain is bounded, that the losses are Lipschitz, or both. In this paper, we develop a new setting for online learning with unbounded domains and non-Lipschitz losses. For this setting we provide an algorithm which guarantees $R_{T}(u)\le \tilde O(G\|u\|\sqrt{T}+L\|u\|^{2}\sqrt{T})$ regret on any problem where the subgradients satisfy $\|g_{t}\|\le G+L\|w_{t}\|$, and show that this bound is unimprovable without further assumptions. We leverage this algorithm to develop new saddle-point optimization algorithms that converge in duality gap in unbounded domains, even in the absence of meaningful curvature. Finally, we provide the first algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses, as well as a matching lower bound. The regret of our dynamic regret algorithm automatically improves to a novel $L^{*}$ bound when the losses are smooth.
We propose a novel $K$-nearest neighbor resampling procedure for estimating the performance of a policy from historical data containing realized episodes of a decision process generated under a different policy. We focus on feedback policies that depend deterministically on the current state in environments with continuous state-action spaces and system-inherent stochasticity effected by chosen actions. Such settings are common in a wide range of high-stake applications and are actively investigated in the context of stochastic control. Our procedure exploits that similar state/action pairs (in a metric sense) are associated with similar rewards and state transitions. This enables our resampling procedure to tackle the counterfactual estimation problem underlying off-policy evaluation (OPE) by simulating trajectories similarly to Monte Carlo methods. Compared to other OPE methods, our algorithm does not require optimization, can be efficiently implemented via tree-based nearest neighbor search and parallelization and does not explicitly assume a parametric model for the environment's dynamics. These properties make the proposed resampling algorithm particularly useful for stochastic control environments. We prove that our method is statistically consistent in estimating the performance of a policy in the OPE setting under weak assumptions and for data sets containing entire episodes rather than independent transitions. To establish the consistency, we generalize Stone's Theorem, a well-known result in nonparametric statistics on local averaging, to include episodic data and the counterfactual estimation underlying OPE. Numerical experiments demonstrate the effectiveness of the algorithm in a variety of stochastic control settings including a linear quadratic regulator, trade execution in limit order books and online stochastic bin packing.
Offline reinforcement learning (RL) offers an appealing approach to real-world tasks by learning policies from pre-collected datasets without interacting with the environment. However, the performance of existing offline RL algorithms heavily depends on the scale and state-action space coverage of datasets. Real-world data collection is often expensive and uncontrollable, leading to small and narrowly covered datasets and posing significant challenges for practical deployments of offline RL. In this paper, we provide a new insight that leveraging the fundamental symmetry of system dynamics can substantially enhance offline RL performance under small datasets. Specifically, we propose a Time-reversal symmetry (T-symmetry) enforced Dynamics Model (TDM), which establishes consistency between a pair of forward and reverse latent dynamics. TDM provides both well-behaved representations for small datasets and a new reliability measure for OOD samples based on compliance with the T-symmetry. These can be readily used to construct a new offline RL algorithm (TSRL) with less conservative policy constraints and a reliable latent space data augmentation procedure. Based on extensive experiments, we find TSRL achieves great performance on small benchmark datasets with as few as 1% of the original samples, which significantly outperforms the recent offline RL algorithms in terms of data efficiency and generalizability.
Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.
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