We propose a novel algorithmic framework for distributional reinforcement learning, based on learning finite-dimensional mean embeddings of return distributions. We derive several new algorithms for dynamic programming and temporal-difference learning based on this framework, provide asymptotic convergence theory, and examine the empirical performance of the algorithms on a suite of tabular tasks. Further, we show that this approach can be straightforwardly combined with deep reinforcement learning, and obtain a new deep RL agent that improves over baseline distributional approaches on the Arcade Learning Environment.
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In distributed deep learning with data parallelism, synchronizing gradients at each training step can cause a huge communication overhead, especially when many nodes work together to train large models. Local gradient methods, such as Local SGD, address this issue by allowing workers to compute locally for $H$ steps without synchronizing with others, hence reducing communication frequency. While $H$ has been viewed as a hyperparameter to trade optimization efficiency for communication cost, recent research indicates that setting a proper $H$ value can lead to generalization improvement. Yet, selecting a proper $H$ is elusive. This work proposes a theory-grounded method for determining $H$, named the Quadratic Synchronization Rule (QSR), which recommends dynamically setting $H$ in proportion to $\frac{1}{\eta^2}$ as the learning rate $\eta$ decays over time. Extensive ImageNet experiments on ResNet and ViT show that local gradient methods with QSR consistently improve the test accuracy over other synchronization strategies. Compared with the standard data parallel training, QSR enables Local AdamW on ViT-B to cut the training time on 16 or 64 GPUs down from 26.7 to 20.2 hours or from 8.6 to 5.5 hours and, at the same time, achieves $1.16\%$ or $0.84\%$ higher top-1 validation accuracy.
Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs), due to complex geometries, interactions between physical variables, and the lack of large amounts of high-resolution training data. To address these issues, we propose Codomain Attention Neural Operator (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to the function space. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations and fluid-structure interactions, we found CoDA-NO to outperform existing methods on the few-shot learning task by over $36\%$. The code is available at //github.com/ashiq24/CoDA-NO.
The emergence of differentiable simulators enabling analytic gradient computation has motivated a new wave of learning algorithms that hold the potential to significantly increase sample efficiency over traditional Reinforcement Learning (RL) methods. While recent research has demonstrated performance gains in scenarios with comparatively smooth dynamics and, thus, smooth optimization landscapes, research on leveraging differentiable simulators for contact-rich scenarios, such as legged locomotion, is scarce. This may be attributed to the discontinuous nature of contact, which introduces several challenges to optimizing with analytic gradients. The purpose of this paper is to determine if analytic gradients can be beneficial even in the face of contact. Our investigation focuses on the effects of different soft and hard contact models on the learning process, examining optimization challenges through the lens of contact simulation. We demonstrate the viability of employing analytic gradients to learn physically plausible locomotion skills with a quadrupedal robot using Short-Horizon Actor-Critic (SHAC), a learning algorithm leveraging analytic gradients, and draw a comparison to a state-of-the-art RL algorithm, Proximal Policy Optimization (PPO), to understand the benefits of analytic gradients.
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare computationally pseudorandom quantum states, an exponential improvement over the previously known bound. This bound is asymptotically tight if linear-time quantum-secure pseudorandom functions exist. - Given an $n$-qubit pure quantum state $|\psi\rangle$ that has fidelity at least $\tau$ with some stabilizer state, we give an algorithm that outputs a succinct description of a stabilizer state that witnesses fidelity at least $\tau - \varepsilon$. The algorithm uses $O(n/(\varepsilon^2\tau^4))$ samples and $\exp\left(O(n/\tau^4)\right) / \varepsilon^2$ time. In the regime of $\tau$ constant, this algorithm estimates stabilizer fidelity substantially faster than the na\"ive $\exp(O(n^2))$-time brute-force algorithm over all stabilizer states. - In the special case of $\tau > \cos^2(\pi/8)$, we show that a modification of the above algorithm runs in polynomial time. - We exhibit a tolerant property testing algorithm for stabilizer states. The underlying algorithmic primitive in all of our results is Bell difference sampling. To prove our results, we establish and/or strengthen connections between Bell difference sampling, symplectic Fourier analysis, and graph theory.
Contrastive learning models have achieved great success in unsupervised visual representation learning, which maximize the similarities between feature representations of different views of the same image, while minimize the similarities between feature representations of views of different images. In text summarization, the output summary is a shorter form of the input document and they have similar meanings. In this paper, we propose a contrastive learning model for supervised abstractive text summarization, where we view a document, its gold summary and its model generated summaries as different views of the same mean representation and maximize the similarities between them during training. We improve over a strong sequence-to-sequence text generation model (i.e., BART) on three different summarization datasets. Human evaluation also shows that our model achieves better faithfulness ratings compared to its counterpart without contrastive objectives.
Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling applications, in which various molecular representations with different symmetry properties and levels of abstraction exist. This review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction, and quantum chemistry. Emphasis is placed on the relevance of the learned molecular features and their complementarity to well-established molecular descriptors. This review provides an overview of current challenges and opportunities, and presents a forecast of the future of GDL for molecular sciences.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.
We propose a new method for event extraction (EE) task based on an imitation learning framework, specifically, inverse reinforcement learning (IRL) via generative adversarial network (GAN). The GAN estimates proper rewards according to the difference between the actions committed by the expert (or ground truth) and the agent among complicated states in the environment. EE task benefits from these dynamic rewards because instances and labels yield to various extents of difficulty and the gains are expected to be diverse -- e.g., an ambiguous but correctly detected trigger or argument should receive high gains -- while the traditional RL models usually neglect such differences and pay equal attention on all instances. Moreover, our experiments also demonstrate that the proposed framework outperforms state-of-the-art methods, without explicit feature engineering.
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