Contextual Online Decision Making with Infinite-Dimensional Functional Regression
Authors: Haichen Hu, Rui Ai, Stephen Bates, David Simchi-Levi
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we propose a universal algorithmic framework that learns the full underlying distribution, enabling a unified approach to all contextual online decision-making problems. The challenge lies in the uncountably infinite-dimensional regression, where existing contextual bandit algorithms all yield infinite regret. We innovatively propose an efficient infinite-dimensional functional regression oracle for contextual cumulative distribution functions (CDFs) and model every datum as a combination of context-dependent CDF basis functions. Our analysis reveals that the decay rate of the eigenvalue sequence of the design integral operator governs the regression error rate, and consequently, the utility regret rate. Specifically, when the eigenvalue sequence exhibits a polynomial decay of order 1 γ 1, the utility regret is bounded by e O T 3γ+2 2(γ+2) . The case that γ = 0 can recover the existing optimal rate in contextual bandits literature with finite-dimensional regression and so as exponential decay. We also provide a numerical method to compute the eigenvalue sequence of integral operators, enabling the practical implementation of our framework. |
| Researcher Affiliation | Academia | 1Center for Computational Science and Engineering, MIT, Cambridge, United States 2Department of CEE, MIT, Cambridge, United States 3Institute for Data, Systems, and Society, MIT, Cambridge, United States 4Department of EECS, MIT, Cambridge, United States. Correspondence to: Haichen Hu <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Regression Oracle: Func Reg Algorithm 2 Stochastic Contextual Decision Making with Infinite Functional Regression |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code for the methodology described, nor does it provide links to repositories or mention code in supplementary materials. |
| Open Datasets | No | The paper discusses a theoretical model and algorithms for online decision-making. It mentions "dataset D = {(xj, aj, yj)}n j=1" abstractly but does not specify any particular publicly available dataset, nor does it provide any concrete access information for one. |
| Dataset Splits | No | The paper's theoretical framework describes data being generated "i.i.d. from some unknown distribution QX" and "i.i.d. data gathered from the last epoch". It does not specify concrete training, test, or validation splits for any particular dataset. |
| Hardware Specification | No | The paper does not provide any specific hardware details used for running experiments. It focuses on theoretical development and algorithms. |
| Software Dependencies | No | The paper discusses theoretical algorithms and numerical methods but does not list any specific software dependencies with version numbers (e.g., libraries, frameworks, or programming language versions) that would be required to reproduce computational results. |
| Experiment Setup | No | The paper describes theoretical algorithms and their properties but does not include an experimental setup section with specific hyperparameters or training configurations. |