Learning with pointwise constraints Ignacio Hounie

Format:

Book

Thesis/Dissertation

Author/Creator:

Hounie, Ignacio, author.

Contributor:

University of Pennsylvania. Electrical and Systems Engineering., degree granting institution.

Language:

English

Subjects (All):

Computer science.

Information science.

0984.

0723.

0800.

Local Subjects:

Computer science.

Information science.

0984.

0723.

0800.

Genre:

Academic theses

Physical Description:

1 online resource (302 pages)

Contained In:

Dissertations Abstracts International 87-12A

Place of Publication:

Ann Arbor : ProQuest Dissertations and Theses, 2026

Language Note:

English

Summary:

Modern AI systems are typically trained by optimizing average losses. This paradigm has enabled unprecedented performance across perception, control, and decision-making tasks. Yet, many of the requirements that matter in practice are not, inherently, averages. Safety, robustness, fairness, alignment, and invariance often describe conditions that should hold across inputs, across parts of an output, or across transformations of the data. When such requirements are enforced on average, a model may still fail systematically on difficult or under-represented cases. As AI systems are increasingly deployed scenarios where these failures can have consequential implications, it becomes necessary to develop learning frameworks that express requirements with finer granularity than an expected risk.This dissertation addresses this issue through the study of pointwise constrained learning. The central premise is that many learning requirements are better expressed over the data itself than through aggregate statistics. Therefore, we develop a pointwise perspective on constrained learning in which the objective may remain an expected risk, but the requirements are imposed locally: at individual timesteps of a sequence, over input transformations, or - more generally - almost everywhere over input-output pairs. This approach changes the structure of the learning problem in a fundamental way. It raises new questions about generalization, because finite samples only partially observe the domain over which the constraints must hold, and it raises new algorithmic questions, because pointwise requirements are often too strict to be imposed without some form of learned relaxation.The first part of the dissertation develops the theoretical foundations of this approach. It formalizes learning with pointwise constraints, shows why classical average-case constrained learning theory does not transfer directly, and studies the dual formulations needed to characterize learnability in this setting. It then develops a general framework for learned relaxations, showing how constraint specifications can be adapted systematically rather than relying on either a priori knowledge about the data or extensive hyperparameter tuning. Together, these results provide both an understanding of when pointwise requirements can be learned from finite samples and also algorithmic tools to relax these requirements when exact feasibility is too restrictive.The second part of the dissertation develops this perspective in a sequence of application-driven settings. It studies pointwise constrained fine-tuning for language models, where per-sample requirements lead to optimization problems that differ fundamentally from average constraints and fixed penalties. It then proposes feasible learning, a limiting case in which the requirement itself becomes the learning problem and there is no separate average objective. Finally, it studies structured data-indexed constraints in long-term time-series forecasting, where errors are controlled across timesteps, and in automatic data augmentation, where invariance requirements induce constraints over input transformations. Across these settings, the dissertation shows that moving from average constraints to pointwise constraints changes both the questions we ask about learning and the algorithms we need to solve them. Most importantly, this framework forces an explicit accounting of what requirements must hold across which data, while also providing tools for how to operationalize those requirements in practice

Notes:

Source: Dissertations Abstracts International, Volume: 87-12, Section: A.

Advisors: Ribeiro, Alejandro Committee members: Pappas, George J.; Hassani, Hamed; Chamon, Luiz F. O.

Ph.D. University of Pennsylvania 2026

Vendor supplied data

Local Notes:

School code: 0175

ISBN:

9798247973683

Access Restriction:

Restricted for use by site license