In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete distribution of the random return (denoted $\eta^\pi$) attained by a given policy $\pi$. We use the certainty-equivalence method to construct our estimator $\hat\eta^\pi$, given a generative model is available. We show that in this circumstance we need a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\epsilon^{2p}(1-\gamma)^{2p+2}}\right)$ to guarantee a $p$-Wasserstein metric between $\hat\eta^\pi$ and $\eta^\pi$ is less than $\epsilon$ with high probability. This implies the distributional policy evaluation problem can be solved with sample efficiency. Also, we show that under different mild assumptions a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\epsilon^{2}(1-\gamma)^{4}}\right)$ suffices to ensure the Kolmogorov metric and total variation metric between $\hat\eta^\pi$ and $\eta^\pi$ is below $\epsilon$ with high probability. Furthermore, we investigate the asymptotic behavior of $\hat\eta^\pi$. We demonstrate that the ``empirical process'' $\sqrt{n}(\hat\eta^\pi-\eta^\pi)$ converges weakly to a Gaussian process in the space of bounded functionals on Lipschitz function class $\ell^\infty(\mathcal{F}_{W_1})$, also in the space of bounded functionals on indicator function class $\ell^\infty(\mathcal{F}_{\mathrm{KS}})$ and bounded measurable function class $\ell^\infty(\mathcal{F}_{\mathrm{TV}})$ when some mild conditions hold. Our findings give rise to a unified approach to statistical inference of a wide class of statistical functionals of $\eta^\pi$.
相關內容
Inference, especially those derived from inductive processes, is a crucial component in our conversation to complement the information implicitly or explicitly conveyed by a speaker. While recent large language models show remarkable advances in inference tasks, their performance in inductive reasoning, where not all information is present in the context, is far behind deductive reasoning. In this paper, we analyze the behavior of the models based on the task difficulty defined by the semantic information gap -- which distinguishes inductive and deductive reasoning (Johnson-Laird, 1988, 1993). Our analysis reveals that the disparity in information between dialogue contexts and desired inferences poses a significant challenge to the inductive inference process. To mitigate this information gap, we investigate a contrastive learning approach by feeding negative samples. Our experiments suggest negative samples help models understand what is wrong and improve their inference generations.
We study fair multi-objective reinforcement learning in which an agent must learn a policy that simultaneously achieves high reward on multiple dimensions of a vector-valued reward. Motivated by the fair resource allocation literature, we model this as an expected welfare maximization problem, for some nonlinear fair welfare function of the vector of long-term cumulative rewards. One canonical example of such a function is the Nash Social Welfare, or geometric mean, the log transform of which is also known as the Proportional Fairness objective. We show that even approximately optimal optimization of the expected Nash Social Welfare is computationally intractable even in the tabular case. Nevertheless, we provide a novel adaptation of Q-learning that combines nonlinear scalarized learning updates and non-stationary action selection to learn effective policies for optimizing nonlinear welfare functions. We show that our algorithm is provably convergent, and we demonstrate experimentally that our approach outperforms techniques based on linear scalarization, mixtures of optimal linear scalarizations, or stationary action selection for the Nash Social Welfare Objective.
In this paper, we present a nonlinear analysis software toolkit, which can help in biomechanical gait data analysis by implementing various nonlinear statistical analysis algorithms. The toolkit is proposed to tackle the need for an easy-to-use and friendly analyzer for gait data where algorithms seem complex to implement in software and execute. With the availability of our toolkit, people without programming knowledge can run the analysis to receive human gait data analysis results. Our toolkit includes the implementation of several nonlinear analysis algorithms, while it is also possible for users with programming experience to expand its scope by implementing and adding more algorithms to the toolkit. Currently, the toolkit supports MatLab bindings while being developed in Python. The toolkit can seamlessly run as a background process to analyze hundreds of different gait data and produce analysis outcomes and figures that illustrate these results.
The first part of this thesis focuses on maximizing the overall recommendation accuracy. This accuracy is usually evaluated with some user-oriented metric tailored to the recommendation scenario, but because recommendation is usually treated as a machine learning problem, recommendation models are trained to maximize some other generic criteria that does not necessarily align with the criteria ultimately captured by the user-oriented evaluation metric. Recent research aims at bridging this gap between training and evaluation via direct ranking optimization, but still assumes that the metric used for evaluation should also be the metric used for training. We challenge this assumption, mainly because some metrics are more informative than others. Indeed, we show that models trained via the optimization of a loss inspired by Rank-Biased Precision (RBP) tend to yield higher accuracy, even when accuracy is measured with metrics other than RBP. However, the superiority of this RBP-inspired loss stems from further benefiting users who are already well-served, rather than helping those who are not. This observation inspires the second part of this thesis, where our focus turns to helping non-mainstream users. These are users who are difficult to recommend to either because there is not enough data to model them, or because they have niche taste and thus few similar users to look at when recommending in a collaborative way. These differences in mainstreamness introduce a bias reflected in an accuracy gap between users or user groups, which we try to narrow.
The emerging field of quantum machine learning has the potential of revolutionizing our perspectives of quantum computing and artificial intelligence. In the predominantly empirical realm of quantum machine learning, a theoretical void persists. This paper addresses the gap by highlighting the quantum cross entropy, a pivotal counterpart to the classical cross entropy. We establish quantum cross entropy's role in quantum data compression, a fundamental machine learning task, by demonstrating that it acts as the compression rate for sub-optimal quantum source coding. Our approach involves a novel, universal quantum data compression protocol based on the quantum generalization of variable-length coding and the principle of quantum strong typicality. This reveals that quantum cross entropy can effectively serve as a loss function in quantum machine learning algorithms. Furthermore, we illustrate that the minimum of quantum cross entropy aligns with the von Neumann entropy, reinforcing its role as the optimal compression rate and underscoring its significance in advancing our understanding of quantum machine learning's theoretical framework.
In this study, we present an investigation into the anisotropy dynamics and intrinsic dimension of embeddings in transformer architectures, focusing on the dichotomy between encoders and decoders. Our findings reveal that the anisotropy profile in transformer decoders exhibits a distinct bell-shaped curve, with the highest anisotropy concentrations in the middle layers. This pattern diverges from the more uniformly distributed anisotropy observed in encoders. In addition, we found that the intrinsic dimension of embeddings increases in the initial phases of training, indicating an expansion into higher-dimensional space. Which is then followed by a compression phase towards the end of training with dimensionality decrease, suggesting a refinement into more compact representations. Our results provide fresh insights to the understanding of encoders and decoders embedding properties.
We propose a multi-agent reinforcement learning dynamics, and analyze its convergence in infinite-horizon discounted Markov potential games. We focus on the independent and decentralized setting, where players do not have knowledge of the game model and cannot coordinate. In each stage, players update their estimate of Q-function that evaluates their total contingent payoff based on the realized one-stage reward in an asynchronous manner. Then, players independently update their policies by incorporating an optimal one-stage deviation strategy based on the estimated Q-function. A key feature of the learning dynamics is that the Q-function estimates are updated at a faster timescale than the policies. We prove that the policies induced by our learning dynamics converge to the set of stationary Nash equilibria in Markov potential games with probability 1. Our results highlight the efficacy of simple learning dynamics in reaching to the set of stationary Nash equilibrium even in environments with minimal information available.
Contrastive loss has been increasingly used in learning representations from multiple modalities. In the limit, the nature of the contrastive loss encourages modalities to exactly match each other in the latent space. Yet it remains an open question how the modality alignment affects the downstream task performance. In this paper, based on an information-theoretic argument, we first prove that exact modality alignment is sub-optimal in general for downstream prediction tasks. Hence we advocate that the key of better performance lies in meaningful latent modality structures instead of perfect modality alignment. To this end, we propose three general approaches to construct latent modality structures. Specifically, we design 1) a deep feature separation loss for intra-modality regularization; 2) a Brownian-bridge loss for inter-modality regularization; and 3) a geometric consistency loss for both intra- and inter-modality regularization. Extensive experiments are conducted on two popular multi-modal representation learning frameworks: the CLIP-based two-tower model and the ALBEF-based fusion model. We test our model on a variety of tasks including zero/few-shot image classification, image-text retrieval, visual question answering, visual reasoning, and visual entailment. Our method achieves consistent improvements over existing methods, demonstrating the effectiveness and generalizability of our proposed approach on latent modality structure regularization.
Transformer is a promising neural network learner, and has achieved great success in various machine learning tasks. Thanks to the recent prevalence of multimodal applications and big data, Transformer-based multimodal learning has become a hot topic in AI research. This paper presents a comprehensive survey of Transformer techniques oriented at multimodal data. The main contents of this survey include: (1) a background of multimodal learning, Transformer ecosystem, and the multimodal big data era, (2) a theoretical review of Vanilla Transformer, Vision Transformer, and multimodal Transformers, from a geometrically topological perspective, (3) a review of multimodal Transformer applications, via two important paradigms, i.e., for multimodal pretraining and for specific multimodal tasks, (4) a summary of the common challenges and designs shared by the multimodal Transformer models and applications, and (5) a discussion of open problems and potential research directions for the community.
Rehearsal, seeking to remind the model by storing old knowledge in lifelong learning, is one of the most effective ways to mitigate catastrophic forgetting, i.e., biased forgetting of previous knowledge when moving to new tasks. However, the old tasks of the most previous rehearsal-based methods suffer from the unpredictable domain shift when training the new task. This is because these methods always ignore two significant factors. First, the Data Imbalance between the new task and old tasks that makes the domain of old tasks prone to shift. Second, the Task Isolation among all tasks will make the domain shift toward unpredictable directions; To address the unpredictable domain shift, in this paper, we propose Multi-Domain Multi-Task (MDMT) rehearsal to train the old tasks and new task parallelly and equally to break the isolation among tasks. Specifically, a two-level angular margin loss is proposed to encourage the intra-class/task compactness and inter-class/task discrepancy, which keeps the model from domain chaos. In addition, to further address domain shift of the old tasks, we propose an optional episodic distillation loss on the memory to anchor the knowledge for each old task. Experiments on benchmark datasets validate the proposed approach can effectively mitigate the unpredictable domain shift.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191