Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Game

Offline reinforcement learning (RL) aims at learning an optimal strategy using a pre-collected dataset without further interactions with the environment. While various algorithms have been proposed for offline RL in the previous literature, the minimax optimal performance has only been (nearly) achieved for tabular Markov decision processes (MDPs). In this paper, we focus on offline RL with linear function approximation and propose two new algorithms, SPEVI+ and SPMVI+, for single-agent MDPs and two-player zero-sum Markov games (MGs), respectively. The proposed algorithms feature carefully crafted data splitting mechanisms and novel variance-reduction pessimistic estimators. Theoretical analysis demonstrates that they are capable of matching the performance lower bounds up to logarithmic factors. As a byproduct, a new performance lower bound is established for MGs, which tightens the existing results. To the best of our knowledge, these are the first computationally efficient and nearly minimax optimal algorithms for offline single-agent MDPs and MGs with linear function approximation.

MulT: An End-to-End Multitask Learning Transformer

We propose an end-to-end Multitask Learning Transformer framework, named MulT, to simultaneously learn multiple high-level vision tasks, including depth estimation, semantic segmentation, reshading, surface normal estimation, 2D keypoint detection, and edge detection. Based on the Swin transformer model, our framework encodes the input image into a shared representation and makes predictions for each vision task using task-specific transformer-based decoder heads. At the heart of our approach is a shared attention mechanism modeling the dependencies across the tasks. We evaluate our model on several multitask benchmarks, showing that our MulT framework outperforms both the state-of-the art multitask convolutional neural network models and all the respective single task transformer models. Our experiments further highlight the benefits of sharing attention across all the tasks, and demonstrate that our MulT model is robust and generalizes well to new domains. Our project website is at https://ivrl.github.io/MulT/.

Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions

We study the linear contextual bandit problem in the presence of adversarial corruption, where the reward at each round is corrupted by an adversary, and the corruption level (i.e., the sum of corruption magnitudes over the horizon) is $C\geq 0$. The best-known algorithms in this setting are limited in that they either are computationally inefficient or require a strong assumption on the corruption, or their regret is at least $C$ times worse than the regret without corruption. In this paper, to overcome these limitations, we propose a new algorithm based on the principle of optimism in the face of uncertainty. At the core of our algorithm is a weighted ridge regression where the weight of each chosen action depends on its confidence up to some threshold. We show that for both known $C$ and unknown $C$ cases, our algorithm with proper choice of hyperparameter achieves a regret that nearly matches the lower bounds. Thus, our algorithm is nearly optimal up to logarithmic factors for both cases. Notably, our algorithm achieves the near-optimal regret for both corrupted and uncorrupted cases ($C=0$) simultaneously.

Leverage Your Local and Global Representations: A New Self-Supervised Learning Strategy

Self-supervised learning (SSL) methods aim to learn view-invariant representations by maximizing the similarity between the features extracted from different crops of the same image regardless of cropping size and content. In essence, this strategy ignores the fact that two crops may truly contain different image information, e.g., background and small objects, and thus tends to restrain the diversity of the learned representations. In this work, we address this issue by introducing a new self-supervised learning strategy, LoGo, that explicitly reasons about Local and Global crops. To achieve view invariance, LoGo encourages similarity between global crops from the same image, as well as between a global and a local crop. However, to correctly encode the fact that the content of smaller crops may differ entirely, LoGo promotes two local crops to have dissimilar representations, while being close to global crops. Our LoGo strategy can easily be applied to existing SSL methods. Our extensive experiments on a variety of datasets and using different self-supervised learning frameworks validate its superiority over existing approaches. Noticeably, we achieve better results than supervised models on transfer learning when using only 1/10 of the data.

Deep Non-rigid Structure-from-Motion: A Sequence-to-Sequence Translation Perspective

Directly regressing the non-rigid shape and camera pose from the individual 2D frame is ill-suited to the Non-Rigid Structure-from-Motion (NRSfM) problem. This frame-by-frame 3D reconstruction pipeline overlooks the inherent spatial-temporal nature of NRSfM, i.e., reconstructing the whole 3D sequence from the input 2D sequence. In this paper, we propose to model deep NRSfM from a sequence-to-sequence translation perspective, where the input 2D frame sequence is taken as a whole to reconstruct the deforming 3D non-rigid shape sequence. First, we apply a shape-motion predictor to estimate the initial non-rigid shape and camera motion from a single frame. Then we propose a context modeling module to model camera motions and complex non-rigid shapes. To tackle the difficulty in enforcing the global structure constraint within the deep framework, we propose to impose the union-of-subspace structure by replacing the self-expressiveness layer with multi-head attention and delayed regularizers, which enables end-to-end batch-wise training. Experimental results across different datasets such as Human3.6M, CMU Mocap and InterHand prove the superiority of our framework. The code will be made publicly available

Non-Linear Reinforcement Learning in Large Action Spaces: Structural Conditions and Sample-efficiency of Posterior Sampling

Provably sample-efficient Reinforcement Learning (RL) with rich observations and function approximation has witnessed tremendous recent progress, particularly when the underlying function approximators are linear. In this linear regime, computationally and statistically efficient methods exist where the potentially infinite state and action spaces can be captured through a known feature embedding, with the sample complexity scaling with the (intrinsic) dimension of these features. When the action space is finite, significantly more sophisticated results allow non-linear function approximation under appropriate structural constraints on the underlying RL problem, permitting for instance, the learning of good features instead of assuming access to them. In this work, we present the first result for non-linear function approximation which holds for general action spaces under a linear embeddability condition, which generalizes all linear and finite action settings. We design a novel optimistic posterior sampling strategy, TS^3 for such problems, and show worst case sample complexity guarantees that scale with a rank parameter of the RL problem, the linear embedding dimension introduced in this work and standard measures of the function class complexity.

RC-MVSNet: Unsupervised Multi-View Stereo with Neural Rendering

Finding accurate correspondences among different views is the Achilles' heel of unsupervised Multi-View Stereo (MVS). Existing methods are built upon the assumption that corresponding pixels share similar photometric features. However, multi-view images in real scenarios observe non-Lambertian surfaces and experience occlusions. In this work, we propose a novel approach with neural rendering (RC-MVSNet) to solve such ambiguity issues of correspondences among views. Specifically, we impose a depth rendering consistency loss to constrain the geometry features close to the object surface to alleviate occlusions. Concurrently, we introduce a reference view synthesis loss to generate consistent supervision, even for non-Lambertian surfaces. Extensive experiments on DTU and Tanks\&Temples benchmarks demonstrate that our RC-MVSNet approach achieves state-of-the-art performance over unsupervised MVS frameworks and competitive performance to many supervised methods.The trained models and code will be released at https://github.com/Boese0601/RC-MVSNet.

Reconfigurable Intelligent Surface Assisted OFDM Relaying: Subcarrier Matching with Balanced SNR

Reconfigurable intelligent surface (RIS) is a promising solution to enhance the performance of wireless communications via reconfiguring the wireless propagation environment. In this paper, we investigate the joint design of RIS passive beamforming and subcarrier matching in RIS-assisted orthogonal frequency division multiplexing (OFDM) dual-hop relaying systems under two cases, depending on the presence of the RIS reflected link from the source to the destination in the first hop. Accordingly, we formulate a mixed-integer nonlinear programming (MINIP) problem to maximize the sum achievable rate over all subcarriers by jointly optimizing the RIS passive beamforming and subcarrier matching. To solve this challenging problem, we first develop a branch-and-bound (BnB)-based alternating optimization algorithm to obtain a near-optimal solution by alternatively optimizing the subcarrier matching by the BnB method and the RIS passive beamforming by using semidefinite relaxation techniques. Then, a low-complexity difference-of-convex penalty-based algorithm is proposed to reduce the computation complexity in the BnB method. To further reduce the computational complexity, we utilize the learning-to-optimize approach to learn the joint design obtained from optimization techniques, which is more amenable to practical implementations. Lastly, computer simulations are presented to evaluate the performance of the proposed algorithms in the two cases. Simulation results demonstrate that the RIS-assisted OFDM relaying system achieves sustainable achievable rate gain as compared to that without RIS, and that with random passive beamforming, since RIS passive beamforming can be leveraged to recast the subcarrier matching among different subcarriers and balance the signal-to-noise ratio within each subcarrier pair.

Pessimistic Minimax Value Iteration: Provably Efficient Equilibrium Learning from Offline Datasets

We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform coverage over all policy pairs, finding an approximate NE involves challenges in three aspects: (i) distributional shift between the behavior policy and the optimal policy, (ii) function approximation to handle large state space, and (iii) minimax optimization for equilibrium solving. We propose a pessimism-based algorithm, dubbed as pessimistic minimax value iteration (PMVI), which overcomes the distributional shift by constructing pessimistic estimates of the value functions for both players and outputs a policy pair by solving NEs based on the two value functions. Furthermore, we establish a data-dependent upper bound on the suboptimality which recovers a sublinear rate without the assumption on uniform coverage of the dataset. We also prove an information-theoretical lower bound, which suggests that the data-dependent term in the upper bound is intrinsic. Our theoretical results also highlight a notion of "relative uncertainty", which characterizes the necessary and sufficient condition for achieving sample efficiency in offline MGs. To the best of our knowledge, we provide the first nearly minimax optimal result for offline MGs with function approximation.

Achieving Minimax Rates in Pool-Based Batch Active Learning

We consider a batch active learning scenario where the learner adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand (pool-based active learning). We analyze a novel stage-wise greedy algorithm and show that, as a function of the label complexity, the excess risk of this algorithm operating in the realizable setting for which we prove matches the known minimax rates in standard statistical learning settings. Our results also exhibit a mild dependence on the batch size. These are the first theoretical results that employ careful trade offs between informativeness and diversity to rigorously quantify the statistical performance of batch active learning in the pool-based scenario.