arXiv subjects

Ambuj Tewari

Publications and source records attributed to Ambuj Tewari.

At least 37 records · Page 2Linked to original sources

arXiv2025

Conformal Robust Control of Linear Systems

End-to-end engineering design pipelines, in which designs are evaluated using concurrently defined optimal controllers, are becoming increasingly common in practice. To discover designs that perform well even under the misspecification of system dynamics, such end-to-end pipelines have now begun evaluating designs with a robust control objective in place of the nominal optimal control setup. Current approaches of specifying such robust control subproblems, however, rely on hand specification of perturbations anticipated to be present upon deployment or margin methods that ignore problem structure, resulting in a lack of theoretical guarantees and overly conservative empirical performance. We, instead, propose a novel methodology for LQR systems that leverages conformal prediction to specify such uncertainty regions in a data-driven fashion. Such regions have distribution-free coverage guarantees on the true system dynamics, in turn allowing for a probabilistic characterization of the regret of the resulting robust controller. We then demonstrate that such a controller can be efficiently produced via a novel policy gradient method that has convergence guarantees. We finally demonstrate the superior empirical performance of our method over alternate robust control specifications, such as $H_{\infty}$ and LQR with multiplicative noise, across a collection of engineering control systems.

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arXiv2025

Learning to Partially Defer for Sequences

In the Learning to Defer (L2D) framework, a prediction model can either make a prediction or defer it to an expert, as determined by a rejector. Current L2D methods train the rejector to decide whether to reject the {\em entire prediction}, which is not desirable when the model predicts long sequences. We present an L2D setting for sequence outputs where the system can defer \textit{specific outputs} of the whole model prediction to an expert in an effort to interleave the expert and machine throughout the prediction. We propose two types of model-based post-hoc rejectors for pre-trained predictors: a token-level rejector, which defers specific token predictions to experts with next token prediction capabilities, and a one-time rejector for experts without such abilities, which defers the remaining sequence from a specific point onward. In the experiments, we also empirically demonstrate that such granular deferrals achieve better cost-accuracy tradeoffs than whole deferrals on Traveling salesman solvers, News summarization, and Weather prediction.

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arXiv2025

Continuum Transformers Perform In-Context Learning by Operator Gradient Descent

Transformers robustly exhibit the ability to perform in-context learning, whereby their predictive accuracy on a task can increase not by parameter updates but merely with the placement of training samples in their context windows. Recent works have shown that transformers achieve this by implementing gradient descent in their forward passes. Such results, however, are restricted to standard transformer architectures, which handle finite-dimensional inputs. In the space of PDE surrogate modeling, a generalization of transformers to handle infinite-dimensional function inputs, known as "continuum transformers," has been proposed and similarly observed to exhibit in-context learning. Despite impressive empirical performance, such in-context learning has yet to be theoretically characterized. We herein demonstrate that continuum transformers perform in-context operator learning by performing gradient descent in an operator RKHS. We demonstrate this using novel proof strategies that leverage a generalized representer theorem for Hilbert spaces and gradient flows over the space of functionals of a Hilbert space. We additionally show the operator learned in context is the Bayes Optimal Predictor in the infinite depth limit of the transformer. We then provide empirical validations of this optimality result and demonstrate that the parameters under which such gradient descent is performed are recovered through the continuum transformer training.

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arXiv2025

Leveraging Offline Data in Linear Latent Contextual Bandits

Leveraging offline data is an attractive way to accelerate online sequential decision-making. However, it is crucial to account for latent states in users or environments in the offline data, and latent bandits form a compelling model for doing so. In this light, we design end-to-end latent bandit algorithms capable of handing uncountably many latent states. We focus on a linear latent contextual bandit $-$ a linear bandit where each user has its own high-dimensional reward parameter in $\mathbb{R}^{d_A}$, but reward parameters across users lie in a low-rank latent subspace of dimension $d_K \ll d_A$. First, we provide an offline algorithm to learn this subspace with provable guarantees. We then present two online algorithms that utilize the output of this offline algorithm to accelerate online learning. The first enjoys $\tilde{O}(\min(d_A\sqrt{T}, d_K\sqrt{T}(1+\sqrt{d_AT/d_KN})))$ regret guarantees, so that the effective dimension is lower when the size $N$ of the offline dataset is larger. We prove a matching lower bound on regret, showing that our algorithm is minimax optimal. The second is a practical algorithm that enjoys only a slightly weaker guarantee, but is computationally efficient. We also establish the efficacy of our methods using experiments on both synthetic data and real-life movie recommendation data from MovieLens. Finally, we theoretically establish the generality of the latent bandit model by proving a de Finetti theorem for stateless decision processes.

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arXiv2025

Quantum Learning Theory Beyond Batch Binary Classification

Arunachalam and de Wolf (2018) showed that the sample complexity of quantum batch learning of boolean functions, in the realizable and agnostic settings, has the same form and order as the corresponding classical sample complexities. In this paper, we extend this, ostensibly surprising, message to batch multiclass learning, online boolean learning, and online multiclass learning. For our online learning results, we first consider an adaptive adversary variant of the classical model of Dawid and Tewari (2022). Then, we introduce the first (to the best of our knowledge) model of online learning with quantum examples.

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arXiv2025

The Complexity of Sequential Prediction in Dynamical Systems

We study the problem of learning to predict the next state of a dynamical system when the underlying evolution function is unknown. Unlike previous work, we place no parametric assumptions on the dynamical system, and study the problem from a learning theory perspective. We define new combinatorial measures and dimensions and show that they quantify the optimal mistake and regret bounds in the realizable and agnostic settings respectively. By doing so, we find that in the realizable setting, the total number of mistakes can grow according to \emph{any} increasing function of the time horizon $T$. In contrast, we show that in the agnostic setting under the commonly studied notion of Markovian regret, the only possible rates are $Θ(T)$ and $\tildeΘ(\sqrt{T})$.

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arXiv2025

Conformal Prediction for Ensembles: Improving Efficiency via Score-Based Aggregation

Distribution-free uncertainty estimation for ensemble methods is increasingly desirable due to the widening deployment of multi-modal black-box predictive models. Conformal prediction is one approach that avoids such distributional assumptions. Methods for conformal aggregation have in turn been proposed for ensembled prediction, where the prediction regions of individual models are merged as to retain coverage guarantees while minimizing conservatism. Merging the prediction regions directly, however, sacrifices structures present in the conformal scores that can further reduce conservatism. We, therefore, propose a novel framework that extends the standard scalar formulation of a score function to a multivariate score that produces more efficient prediction regions. We then demonstrate that such a framework can be efficiently leveraged in both classification and predict-then-optimize regression settings downstream and empirically show the advantage over alternate conformal aggregation methods.

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arXiv2025

Generator-Mediated Bandits: Thompson Sampling for GenAI-Powered Adaptive Interventions

Recent advances in generative artificial intelligence (GenAI) models have enabled the generation of personalized content that adapts to up-to-date user context. While personalized decision systems are often modeled using bandit formulations, the integration of GenAI introduces new structure into otherwise classical sequential learning problems. In GenAI-powered interventions, the agent selects a query, but the environment experiences a stochastic response drawn from the generative model. Standard bandit methods do not explicitly account for this structure, where actions influence rewards only through stochastic, observed treatments. We introduce generator-mediated bandit-Thompson sampling (GAMBITTS), a bandit approach designed for this action/treatment split, using mobile health interventions with large language model-generated text as a motivating case study. GAMBITTS explicitly models both the treatment and reward generation processes, using information in the delivered treatment to accelerate policy learning relative to standard methods. We establish regret bounds for GAMBITTS by decomposing sources of uncertainty in treatment and reward, identifying conditions where it achieves stronger guarantees than standard bandit approaches. In simulation studies, GAMBITTS consistently outperforms conventional algorithms by leveraging observed treatments to more accurately estimate expected rewards.

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arXiv2025

On Next-Token Prediction in LLMs: How End Goals Determine the Consistency of Decoding Algorithms

Probabilistic next-token prediction trained using cross-entropy loss is the basis of most large language models. Given a sequence of previous values, next-token prediction assigns a probability to each possible next value in the vocabulary. There are many ways to use next-token prediction to output token sequences. This paper examines a few of these algorithms (greedy, lookahead, random sampling, and temperature-scaled random sampling) and studies their consistency with respect to various goals encoded as loss functions. Although consistency of surrogate losses with respect to a target loss function is a well researched topic, we are the first to study it in the context of LLMs (to the best of our knowledge). We find that, so long as next-token prediction converges to its true probability distribution, random sampling is consistent with outputting sequences that mimic sampling from the true probability distribution. For the other goals, such as minimizing the 0-1 loss on the entire sequence, we show no polynomial-time algorithm is optimal for all probability distributions and all decoding algorithms studied are only optimal for a subset of probability distributions. When analyzing these results, we see that there is a dichotomy created between the goals of information retrieval and creative generation for the decoding algorithms. This shows that choosing the correct decoding algorithm based on the desired goal is extremely important and many of the ones used are lacking theoretical grounding in numerous scenarios.

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arXiv2025

A Computationally Efficient Algorithm for Infinite-Horizon Average-Reward Linear MDPs

We study reinforcement learning in infinite-horizon average-reward settings with linear MDPs. Previous work addresses this problem by approximating the average-reward setting by discounted setting and employing a value iteration-based algorithm that uses clipping to constrain the span of the value function for improved statistical efficiency. However, the clipping procedure requires computing the minimum of the value function over the entire state space, which is prohibitive since the state space in linear MDP setting can be large or even infinite. In this paper, we introduce a value iteration method with efficient clipping operation that only requires computing the minimum of value functions over the set of states visited by the algorithm. Our algorithm enjoys the same regret bound as the previous work while being computationally efficient, with computational complexity that is independent of the size of the state space.

cs.LG↗

arXiv2025

Understanding Best Subset Selection: A Tale of Two C(omplex)ities

We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. Recently, Guo et al. (2020) showed that the model selection performance of BSS depends on a certain identifiability margin, a measure that captures the model discriminative power of BSS under a general correlation structure that is robust to the design dependence, unlike its computational surrogates such as LASSO, SCAD, MCP, etc. Expanding on this, we further broaden the theoretical understanding of best subset selection in this paper and show that the complexities of the residualized signals, the portion of the signals orthogonal to the true active features, and spurious projections, describing the projection operators associated with the irrelevant features, also play fundamental roles in characterizing the margin condition for model consistency of BSS. In particular, we establish both necessary and sufficient margin conditions depending only on the identifiability margin and the two complexity measures. We also partially extend our sufficiency result to the case of high-dimensional sparse generalized linear models (GLMs).

math.ST↗

arXiv2025

Operator Learning: A Statistical Perspective

Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the solution operators of partial differential equations (PDEs). These methods can also be used to develop black-box simulators to model system behavior from experimental data, even without a known mathematical model. In this article, we begin by formalizing operator learning as a function-to-function regression problem and review some recent developments in the field. We also discuss PDE-specific operator learning, outlining strategies for incorporating physical and mathematical constraints into architecture design and training processes. Finally, we end by highlighting key future directions such as active data collection and the development of rigorous uncertainty quantification frameworks.

stat.ML↗

arXiv2025

Reinforcement Learning for Infinite-Horizon Average-Reward Linear MDPs via Approximation by Discounted-Reward MDPs

We study the problem of infinite-horizon average-reward reinforcement learning with linear Markov decision processes (MDPs). The associated Bellman operator of the problem not being a contraction makes the algorithm design challenging. Previous approaches either suffer from computational inefficiency or require strong assumptions on dynamics, such as ergodicity, for achieving a regret bound of $\widetilde{O}(\sqrt{T})$. In this paper, we propose the first algorithm that achieves $\widetilde{O}(\sqrt{T})$ regret with computational complexity polynomial in the problem parameters, without making strong assumptions on dynamics. Our approach approximates the average-reward setting by a discounted MDP with a carefully chosen discounting factor, and then applies an optimistic value iteration. We propose an algorithmic structure that plans for a nonstationary policy through optimistic value iteration and follows that policy until a specified information metric in the collected data doubles. Additionally, we introduce a value function clipping procedure for limiting the span of the value function for sample efficiency.

stat.ML↗

arXiv2025

Near Optimal Pure Exploration in Logistic Bandits

Bandit algorithms have garnered significant attention due to their practical applications in real-world scenarios. However, beyond simple settings such as multi-arm or linear bandits, optimal algorithms remain scarce. Notably, no optimal solution exists for pure exploration problems in the context of generalized linear model (GLM) bandits. In this paper, we narrow this gap and develop the first track-and-stop algorithm for general pure exploration problems under the logistic bandit called logistic track-and-stop (Log-TS). Log-TS is an efficient algorithm that asymptotically matches an approximation for the instance-specific lower bound of the expected sample complexity up to a logarithmic factor.

stat.ML↗

arXiv2025

Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators

We study learning-theoretic foundations of operator learning, using the linear layer of the Fourier Neural Operator architecture as a model problem. First, we identify three main errors that occur during the learning process: statistical error due to finite sample size, truncation error from finite rank approximation of the operator, and discretization error from handling functional data on a finite grid of domain points. Finally, we analyze a Discrete Fourier Transform (DFT) based least squares estimator, establishing both upper and lower bounds on the aforementioned errors.

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arXiv2025

On the Benefits of Active Data Collection in Operator Learning

We study active data collection strategies for operator learning when the target operator is linear and the input functions are drawn from a mean-zero stochastic process with continuous covariance kernels. With an active data collection strategy, we establish an error convergence rate in terms of the decay rate of the eigenvalues of the covariance kernel. We can achieve arbitrarily fast error convergence rates with sufficiently rapid eigenvalue decay of the covariance kernels. This contrasts with the passive (i.i.d.) data collection strategies, where the convergence rate is never faster than linear decay ($\sim n^{-1}$). In fact, for our setting, we show a \emph{non-vanishing} lower bound for any passive data collection strategy, regardless of the eigenvalues decay rate of the covariance kernel. Overall, our results show the benefit of active data collection strategies in operator learning over their passive counterparts.

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arXiv2024

Generation through the lens of learning theory

We study generation through the lens of statistical learning theory. First, we abstract and formalize the results of Gold [1967], Angluin [1979], Angluin [1980] and Kleinberg and Mullainathan [2024] in terms of a binary hypothesis class defined over an abstract example space. Then, we extend the notion of "generation" from Kleinberg and Mullainathan [2024] to two new settings, we call "uniform" and "non-uniform" generation, and provide a characterization of which hypothesis classes are uniformly and non-uniformly generatable. As is standard in learning theory, our characterizations are in terms of the finiteness of a new combinatorial dimension termed the Closure dimension. By doing so, we are able to compare generatability with predictability (captured via PAC and online learnability) and show that these two properties of hypothesis classes are incompatible -- there are classes that are generatable but not predictable and vice versa. Finally, we extend our results to capture prompted generation and give a complete characterization of which classes are prompt generatable, generalizing some of the work by Kleinberg and Mullainathan [2024].

cs.LG↗

arXiv2024

A Characterization of Multioutput Learnability

We consider the problem of learning multioutput function classes in the batch and online settings. In both settings, we show that a multioutput function class is learnable if and only if each single-output restriction of the function class is learnable. This provides a complete characterization of the learnability of multilabel classification and multioutput regression in both batch and online settings. As an extension, we also consider multilabel learnability in the bandit feedback setting and show a similar characterization as in the full-feedback setting.

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