Keywords

Differentiable optimization, Differentiable optimization, Machine Learning, Predictive Modeling, Structured prediction, Statistical Learning

Abstract

Recent trends in statistical machine learning have revealed the power of integrating optimization procedures as first-class components within end-to-end large-scale predictive systems. These structured computations—often formulated as projections onto geometric objects like polytopes—enable models to inject domain-specific inductive biases and enforce desirable properties in the learned representations useful in downstream classification or regression tasks. This dissertation explores the role of such projections in enhancing learning performance and generalization, particularly in the context of predictive modeling with data intensive systems.

Motivated by the limitations of traditional surrogate loss functions such as logistic loss for classification or cross-entropy for multiclass problems, this work explores several novel, differentiable, projections onto different n-dimensional polytopes. When composed with other system components, these projections yields a family of surrogate objectives that tightly approximates the true, often computationally unfeasible objective. A concrete example presented in later chapters is the use of euclidean projections to $n,k$ hypersimplex, which result in close surrogates to the zero-one loss, yielding greater generalization under large batch regimes.

Beyond the hypersimplex, this dissertation situates the proposed framework within a broader family of polytope projections, examining their computational properties and practical relevance in modern learning pipelines. These structured layers are shown to act as modular components that not only preserve scalability but also enhance interpretability and alignment with task-specific objectives. The findings demonstrate that carefully designed projection-based mechanisms can bridge the gap between theoretically principled objectives and the demands of large-scale optimization—ultimately serving as effective building blocks for robust, generalizable, and domain-aware machine learning systems.

Completion Date

2025

Semester

Fall

Committee Chair

Tang, Liansheng

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Statistics and Data Science

Format

PDF

Identifier

DP0029776

Document Type

Thesis

Campus Location

Orlando (Main) Campus

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