arXiv subjects

Yu Bai

Publications and source records attributed to Yu Bai.

At least 73 records · Page 4Linked to original sources

arXiv2023

Efficient Reinforcement Learning with Impaired Observability: Learning to Act with Delayed and Missing State Observations

In real-world reinforcement learning (RL) systems, various forms of {\it impaired observability} can complicate matters. These situations arise when an agent is unable to observe the most recent state of the system due to latency or lossy channels, yet the agent must still make real-time decisions. This paper introduces a theoretical investigation into efficient RL in control systems where agents must act with delayed and missing state observations. We present algorithms and establish near-optimal regret upper and lower bounds, of the form $\tilde{\mathcal{O}}(\sqrt{{\rm poly}(H) SAK})$, for RL in the delayed and missing observation settings. Here $S$ and $A$ are the sizes of state and action spaces, $H$ is the time horizon and $K$ is the number of episodes. Despite impaired observability posing significant challenges to the policy class and planning, our results demonstrate that learning remains efficient, with the regret bound optimally depending on the state-action size of the original system. Additionally, we provide a characterization of the performance of the optimal policy under impaired observability, comparing it to the optimal value obtained with full observability. Numerical results are provided to support our theory.

cs.LG↗

arXiv2023

How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations

While large language models based on the transformer architecture have demonstrated remarkable in-context learning (ICL) capabilities, understandings of such capabilities are still in an early stage, where existing theory and mechanistic understanding focus mostly on simple scenarios such as learning simple function classes. This paper takes initial steps on understanding ICL in more complex scenarios, by studying learning with representations. Concretely, we construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function, composed with a linear function that differs in each instance. By construction, the optimal ICL algorithm first transforms the inputs by the representation function, and then performs linear ICL on top of the transformed dataset. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size. Empirically, we find trained transformers consistently achieve near-optimal ICL performance in this setting, and exhibit the desired dissection where lower layers transforms the dataset and upper layers perform linear ICL. Through extensive probing and a new pasting experiment, we further reveal several mechanisms within the trained transformers, such as concrete copying behaviors on both the inputs and the representations, linear ICL capability of the upper layers alone, and a post-ICL representation selection mechanism in a harder mixture setting. These observed mechanisms align well with our theory and may shed light on how transformers perform ICL in more realistic scenarios.

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arXiv2023

An Empirical Study of NetOps Capability of Pre-Trained Large Language Models

Nowadays, the versatile capabilities of Pre-trained Large Language Models (LLMs) have attracted much attention from the industry. However, some vertical domains are more interested in the in-domain capabilities of LLMs. For the Networks domain, we present NetEval, an evaluation set for measuring the comprehensive capabilities of LLMs in Network Operations (NetOps). NetEval is designed for evaluating the commonsense knowledge and inference ability in NetOps in a multi-lingual context. NetEval consists of 5,732 questions about NetOps, covering five different sub-domains of NetOps. With NetEval, we systematically evaluate the NetOps capability of 26 publicly available LLMs. The results show that only GPT-4 can achieve a performance competitive to humans. However, some open models like LLaMA 2 demonstrate significant potential.

cs.CL↗

arXiv2023

DePA: Improving Non-autoregressive Machine Translation with Dependency-Aware Decoder

Non-autoregressive machine translation (NAT) models have lower translation quality than autoregressive translation (AT) models because NAT decoders do not depend on previous target tokens in the decoder input. We propose a novel and general Dependency-Aware Decoder (DePA) to enhance target dependency modeling in the decoder of fully NAT models from two perspectives: decoder self-attention and decoder input. First, we propose an autoregressive forward-backward pre-training phase before NAT training, which enables the NAT decoder to gradually learn bidirectional target dependencies for the final NAT training. Second, we transform the decoder input from the source language representation space to the target language representation space through a novel attentive transformation process, which enables the decoder to better capture target dependencies. DePA can be applied to any fully NAT models. Extensive experiments show that DePA consistently improves highly competitive and state-of-the-art fully NAT models on widely used WMT and IWSLT benchmarks by up to 1.88 BLEU gain, while maintaining the inference latency comparable to other fully NAT models.

cs.CL↗

arXiv2023

What can a Single Attention Layer Learn? A Study Through the Random Features Lens

Attention layers -- which map a sequence of inputs to a sequence of outputs -- are core building blocks of the Transformer architecture which has achieved significant breakthroughs in modern artificial intelligence. This paper presents a rigorous theoretical study on the learning and generalization of a single multi-head attention layer, with a sequence of key vectors and a separate query vector as input. We consider the random feature setting where the attention layer has a large number of heads, with randomly sampled frozen query and key matrices, and trainable value matrices. We show that such a random-feature attention layer can express a broad class of target functions that are permutation invariant to the key vectors. We further provide quantitative excess risk bounds for learning these target functions from finite samples, using random feature attention with finitely many heads. Our results feature several implications unique to the attention structure compared with existing random features theory for neural networks, such as (1) Advantages in the sample complexity over standard two-layer random-feature networks; (2) Concrete and natural classes of functions that can be learned efficiently by a random-feature attention layer; and (3) The effect of the sampling distribution of the query-key weight matrix (the product of the query and key matrix), where Gaussian random weights with a non-zero mean result in better sample complexities over the zero-mean counterpart for learning certain natural target functions. Experiments on simulated data corroborate our theoretical findings and further illustrate the interplay between the sample size and the complexity of the target function.

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arXiv2023

Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection

Neural sequence models based on the transformer architecture have demonstrated remarkable \emph{in-context learning} (ICL) abilities, where they can perform new tasks when prompted with training and test examples, without any parameter update to the model. This work first provides a comprehensive statistical theory for transformers to perform ICL. Concretely, we show that transformers can implement a broad class of standard machine learning algorithms in context, such as least squares, ridge regression, Lasso, learning generalized linear models, and gradient descent on two-layer neural networks, with near-optimal predictive power on various in-context data distributions. Using an efficient implementation of in-context gradient descent as the underlying mechanism, our transformer constructions admit mild size bounds, and can be learned with polynomially many pretraining sequences. Building on these ``base'' ICL algorithms, intriguingly, we show that transformers can implement more complex ICL procedures involving \emph{in-context algorithm selection}, akin to what a statistician can do in real life -- A \emph{single} transformer can adaptively select different base ICL algorithms -- or even perform qualitatively different tasks -- on different input sequences, without any explicit prompting of the right algorithm or task. We both establish this in theory by explicit constructions, and also observe this phenomenon experimentally. In theory, we construct two general mechanisms for algorithm selection with concrete examples: pre-ICL testing, and post-ICL validation. As an example, we use the post-ICL validation mechanism to construct a transformer that can perform nearly Bayes-optimal ICL on a challenging task -- noisy linear models with mixed noise levels. Experimentally, we demonstrate the strong in-context algorithm selection capabilities of standard transformer architectures.

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arXiv2023

Sample-Efficient Learning of POMDPs with Multiple Observations In Hindsight

This paper studies the sample-efficiency of learning in Partially Observable Markov Decision Processes (POMDPs), a challenging problem in reinforcement learning that is known to be exponentially hard in the worst-case. Motivated by real-world settings such as loading in game playing, we propose an enhanced feedback model called ``multiple observations in hindsight'', where after each episode of interaction with the POMDP, the learner may collect multiple additional observations emitted from the encountered latent states, but may not observe the latent states themselves. We show that sample-efficient learning under this feedback model is possible for two new subclasses of POMDPs: \emph{multi-observation revealing POMDPs} and \emph{distinguishable POMDPs}. Both subclasses generalize and substantially relax \emph{revealing POMDPs} -- a widely studied subclass for which sample-efficient learning is possible under standard trajectory feedback. Notably, distinguishable POMDPs only require the emission distributions from different latent states to be \emph{different} instead of \emph{linearly independent} as required in revealing POMDPs.

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arXiv2023

Automatic Speech Recognition of Non-Native Child Speech for Language Learning Applications

Voicebots have provided a new avenue for supporting the development of language skills, particularly within the context of second language learning. Voicebots, though, have largely been geared towards native adult speakers. We sought to assess the performance of two state-of-the-art ASR systems, Wav2Vec2.0 and Whisper AI, with a view to developing a voicebot that can support children acquiring a foreign language. We evaluated their performance on read and extemporaneous speech of native and non-native Dutch children. We also investigated the utility of using ASR technology to provide insight into the children's pronunciation and fluency. The results show that recent, pre-trained ASR transformer-based models achieve acceptable performance from which detailed feedback on phoneme pronunciation quality can be extracted, despite the challenging nature of child and non-native speech.

cs.CL↗

arXiv2023

An ASR-Based Tutor for Learning to Read: How to Optimize Feedback to First Graders

The interest in employing automatic speech recognition (ASR) in applications for reading practice has been growing in recent years. In a previous study, we presented an ASR-based Dutch reading tutor application that was developed to provide instantaneous feedback to first-graders learning to read. We saw that ASR has potential at this stage of the reading process, as the results suggested that pupils made progress in reading accuracy and fluency by using the software. In the current study, we used children's speech from an existing corpus (JASMIN) to develop two new ASR systems, and compared the results to those of the previous study. We analyze correct/incorrect classification of the ASR systems using human transcripts at word level, by means of evaluation measures such as Cohen's Kappa, Matthews Correlation Coefficient (MCC), precision, recall and F-measures. We observe improvements for the newly developed ASR systems regarding the agreement with human-based judgment and correct rejection (CR). The accuracy of the ASR systems varies for different reading tasks and word types. Our results suggest that, in the current configuration, it is difficult to classify isolated words. We discuss these results, possible ways to improve our systems and avenues for future research.

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arXiv2023

Near-Optimal Learning of Extensive-Form Games with Imperfect Information

This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only $\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$ episodes of play to find an $\varepsilon$-approximate Nash equilibrium in two-player zero-sum games, where $X,Y$ are the number of information sets and $A,B$ are the number of actions for the two players. This improves upon the best known sample complexity of $\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$ by a factor of $\widetilde{\mathcal{O}}(\max\{X, Y\})$, and matches the information-theoretic lower bound up to logarithmic factors. We achieve this sample complexity by two new algorithms: Balanced Online Mirror Descent, and Balanced Counterfactual Regret Minimization. Both algorithms rely on novel approaches of integrating \emph{balanced exploration policies} into their classical counterparts. We also extend our results to learning Coarse Correlated Equilibria in multi-player general-sum games.

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arXiv2023

Breaking the Curse of Multiagency: Provably Efficient Decentralized Multi-Agent RL with Function Approximation

A unique challenge in Multi-Agent Reinforcement Learning (MARL) is the curse of multiagency, where the description length of the game as well as the complexity of many existing learning algorithms scale exponentially with the number of agents. While recent works successfully address this challenge under the model of tabular Markov Games, their mechanisms critically rely on the number of states being finite and small, and do not extend to practical scenarios with enormous state spaces where function approximation must be used to approximate value functions or policies. This paper presents the first line of MARL algorithms that provably resolve the curse of multiagency under function approximation. We design a new decentralized algorithm -- V-Learning with Policy Replay, which gives the first polynomial sample complexity results for learning approximate Coarse Correlated Equilibria (CCEs) of Markov Games under decentralized linear function approximation. Our algorithm always outputs Markov CCEs, and achieves an optimal rate of $\widetilde{\mathcal{O}}(ε^{-2})$ for finding $ε$-optimal solutions. Also, when restricted to the tabular case, our result improves over the current best decentralized result $\widetilde{\mathcal{O}}(ε^{-3})$ for finding Markov CCEs. We further present an alternative algorithm -- Decentralized Optimistic Policy Mirror Descent, which finds policy-class-restricted CCEs using a polynomial number of samples. In exchange for learning a weaker version of CCEs, this algorithm applies to a wider range of problems under generic function approximation, such as linear quadratic games and MARL problems with low ''marginal'' Eluder dimension.

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arXiv2023

Improved Online Conformal Prediction via Strongly Adaptive Online Learning

We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop new online conformal prediction methods that minimize the strongly adaptive regret, which measures the worst-case regret over all intervals of a fixed length. We prove that our methods achieve near-optimal strongly adaptive regret for all interval lengths simultaneously, and approximately valid coverage. Experiments show that our methods consistently obtain better coverage and smaller prediction sets than existing methods on real-world tasks, such as time series forecasting and image classification under distribution shift.

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arXiv2023

Offline Learning in Markov Games with General Function Approximation

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

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arXiv2023

Lower Bounds for Learning in Revealing POMDPs

This paper studies the fundamental limits of reinforcement learning (RL) in the challenging \emph{partially observable} setting. While it is well-established that learning in Partially Observable Markov Decision Processes (POMDPs) requires exponentially many samples in the worst case, a surge of recent work shows that polynomial sample complexities are achievable under the \emph{revealing condition} -- A natural condition that requires the observables to reveal some information about the unobserved latent states. However, the fundamental limits for learning in revealing POMDPs are much less understood, with existing lower bounds being rather preliminary and having substantial gaps from the current best upper bounds. We establish strong PAC and regret lower bounds for learning in revealing POMDPs. Our lower bounds scale polynomially in all relevant problem parameters in a multiplicative fashion, and achieve significantly smaller gaps against the current best upper bounds, providing a solid starting point for future studies. In particular, for \emph{multi-step} revealing POMDPs, we show that (1) the latent state-space dependence is at least $Ω(S^{1.5})$ in the PAC sample complexity, which is notably harder than the $\widetildeΘ(S)$ scaling for fully-observable MDPs; (2) Any polynomial sublinear regret is at least $Ω(T^{2/3})$, suggesting its fundamental difference from the \emph{single-step} case where $\widetilde{O}(\sqrt{T})$ regret is achievable. Technically, our hard instance construction adapts techniques in \emph{distribution testing}, which is new to the RL literature and may be of independent interest.

cs.LG↗

arXiv2022

Partially Observable RL with B-Stability: Unified Structural Condition and Sharp Sample-Efficient Algorithms

Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal policy under partial observability is known to be hard in the worst case due to an exponential sample complexity lower bound. Recent work has identified several tractable subclasses that are learnable with polynomial samples, such as Partially Observable Markov Decision Processes (POMDPs) with certain revealing or decodability conditions. However, this line of research is still in its infancy, where (1) unified structural conditions enabling sample-efficient learning are lacking; (2) existing sample complexities for known tractable subclasses are far from sharp; and (3) fewer sample-efficient algorithms are available than in fully observable RL. This paper advances all three aspects above for Partially Observable RL in the general setting of Predictive State Representations (PSRs). First, we propose a natural and unified structural condition for PSRs called \emph{B-stability}. B-stable PSRs encompasses the vast majority of known tractable subclasses such as weakly revealing POMDPs, low-rank future-sufficient POMDPs, decodable POMDPs, and regular PSRs. Next, we show that any B-stable PSR can be learned with polynomial samples in relevant problem parameters. When instantiated in the aforementioned subclasses, our sample complexities improve substantially over the current best ones. Finally, our results are achieved by three algorithms simultaneously: Optimistic Maximum Likelihood Estimation, Estimation-to-Decisions, and Model-Based Optimistic Posterior Sampling. The latter two algorithms are new for sample-efficient learning of POMDPs/PSRs.

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arXiv2022

Identifying good directions to escape the NTK regime and efficiently learn low-degree plus sparse polynomials

A recent goal in the theory of deep learning is to identify how neural networks can escape the "lazy training," or Neural Tangent Kernel (NTK) regime, where the network is coupled with its first order Taylor expansion at initialization. While the NTK is minimax optimal for learning dense polynomials (Ghorbani et al, 2021), it cannot learn features, and hence has poor sample complexity for learning many classes of functions including sparse polynomials. Recent works have thus aimed to identify settings where gradient based algorithms provably generalize better than the NTK. One such example is the "QuadNTK" approach of Bai and Lee (2020), which analyzes the second-order term in the Taylor expansion. Bai and Lee (2020) show that the second-order term can learn sparse polynomials efficiently; however, it sacrifices the ability to learn general dense polynomials. In this paper, we analyze how gradient descent on a two-layer neural network can escape the NTK regime by utilizing a spectral characterization of the NTK (Montanari and Zhong, 2020) and building on the QuadNTK approach. We first expand upon the spectral analysis to identify "good" directions in parameter space in which we can move without harming generalization. Next, we show that a wide two-layer neural network can jointly use the NTK and QuadNTK to fit target functions consisting of a dense low-degree term and a sparse high-degree term -- something neither the NTK nor the QuadNTK can do on their own. Finally, we construct a regularizer which encourages our parameter vector to move in the "good" directions, and show that gradient descent on the regularized loss will converge to a global minimizer, which also has low test error. This yields an end to end convergence and generalization guarantee with provable sample complexity improvement over both the NTK and QuadNTK on their own.

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arXiv2022

Stellar chromospheric activities revealed from the LAMOST-K2 time-domain survey

By using the LAMOST time-domain survey data, we study stellar activities based on the $\rm{H_α}$ lines for about 2000 stars in four $K$2 plates. Two indices, $R_{\rm{Hα}}^{'}$ and $R_{\rm{Hα}}^{+}$, are computed from LAMOST spectra, the former of which is derived by excluding the photospheric contributions to the $\rm{H_α}$ lines, while the latter is derived by further subtracting the non-dynamo driven chromospheric emission. Meanwhile, the periodicity and variation amplitudes are computed from \emph{K2} light curves. Both the $R_{\rm{Hα}}^{'}$-Ro relation and $R_{\rm{Hα}}^{+}$-Ro relation show complicated profiles in the non-saturated decay region. Hot stars show flatter slopes and higher activity level than cool stars, and the behaviour is more notable in the $R_{\rm{Hα}}^{+}$-$R_{o}$ relation. This is consistent with recent studies using other activity proxies, including $L_{\rm{x}}/L_{\rm{bol}}$, $R_{\rm{HK}}^{'}$ and amplitudes of optical light curves. % This may suggest different kinds of stars follow different power laws in the decay region. Most of our targets have multiple observations, and some of them exhibit significant variability of ${\rm{Hα}}$ emissions, which may cause the large scatters shown in the decay region. We find three targets exhibiting positive correlation in rotational phase, possibly indicating that their optical light curves are dominated by hot faculae rather than cool starspots.

astro-ph.SR↗

arXiv2022

Efficient Phi-Regret Minimization in Extensive-Form Games via Online Mirror Descent

A conceptually appealing approach for learning Extensive-Form Games (EFGs) is to convert them to Normal-Form Games (NFGs). This approach enables us to directly translate state-of-the-art techniques and analyses in NFGs to learning EFGs, but typically suffers from computational intractability due to the exponential blow-up of the game size introduced by the conversion. In this paper, we address this problem in natural and important setups for the \emph{$Φ$-Hedge} algorithm -- A generic algorithm capable of learning a large class of equilibria for NFGs. We show that $Φ$-Hedge can be directly used to learn Nash Equilibria (zero-sum settings), Normal-Form Coarse Correlated Equilibria (NFCCE), and Extensive-Form Correlated Equilibria (EFCE) in EFGs. We prove that, in those settings, the \emph{$Φ$-Hedge} algorithms are equivalent to standard Online Mirror Descent (OMD) algorithms for EFGs with suitable dilated regularizers, and run in polynomial time. This new connection further allows us to design and analyze a new class of OMD algorithms based on modifying its log-partition function. In particular, we design an improved algorithm with balancing techniques that achieves a sharp $\widetilde{\mathcal{O}}(\sqrt{XAT})$ EFCE-regret under bandit-feedback in an EFG with $X$ information sets, $A$ actions, and $T$ episodes. To our best knowledge, this is the first such rate and matches the information-theoretic lower bound.

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