Related papers: A Closed-Form Upper Bound for Admissible Learning-…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
We study the problem of learning robust classifiers where the classifier will receive a perturbed input. Unlike robust PAC learning studied in prior work, here the clean data and its label are also adversarially chosen. We formulate this…
This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from…
Interpretable and explainable machine learning has seen a recent surge of interest. We focus on safety as a key motivation behind the surge and make the relationship between interpretability and safety more quantitative. Toward assessing…
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
This paper studies systematic exploration for reinforcement learning with rich observations and function approximation. We introduce a new model called contextual decision processes, that unifies and generalizes most prior settings. Our…
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless…
The problem of constructing confidence sets that are adaptive in L^2-loss over a continuous scale of Sobolev classes of probability densities is considered. Adaptation holds, where possible, with respect to both the radius of the Sobolev…
Meta-learning automatically infers an inductive bias by observing data from a number of related tasks. The inductive bias is encoded by hyperparameters that determine aspects of the model class or training algorithm, such as initialization…
Large language models (LLMs) that iteratively revise their outputs through mechanisms such as chain-of-thought reasoning, self-reflection, or multi-agent debate lack principled guarantees regarding the stability of their probability…
Reinforcement learning (RL) for reachability specifications is fundamental in sequential decision-making, yet theoretical guarantees remain less explored. A recent work achieves asymptotic convergence to optimal policies. However, this…
Process Reward Models (PRMs) provide step-level feedback for reasoning, but current PRMs usually output only a single reward score for each step. Downstream methods must therefore treat imperfect step-level reward predictions as reliable…
In this note, we provide upper bounds on the expectation of the supremum of empirical processes indexed by H\"older classes of any smoothness and for any distribution supported on a bounded set in $\mathbb R^d$. These results can be…
The classical perceptron rule provides a varying upper bound on the maximum margin, namely the length of the current weight vector divided by the total number of updates up to that time. Requiring that the perceptron updates its internal…
Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…
Active learning has long been a topic of study in machine learning. However, as increasingly complex and opaque models have become standard practice, the process of active learning, too, has become more opaque. There has been little…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian…
Most modern neural networks for classification fail to take into account the concept of the unknown. Trained neural networks are usually tested in an unrealistic scenario with only examples from a closed set of known classes. In an attempt…