# Limitations of Information-Theoretic Generalization Bounds for Gradient Descent Methods in Stochastic Convex Optimization

@inproceedings{Haghifam2022LimitationsOI, title={Limitations of Information-Theoretic Generalization Bounds for Gradient Descent Methods in Stochastic Convex Optimization}, author={Mahdi Haghifam and Borja Rodr'iguez-G'alvez and Ragnar Thobaben and Mikael Skoglund and Daniel M. Roy and Gintare Karolina Dziugaite}, booktitle={International Conference on Algorithmic Learning Theory}, year={2022} }

To date, no"information-theoretic"frameworks for reasoning about generalization error have been shown to establish minimax rates for gradient descent in the setting of stochastic convex optimization. In this work, we consider the prospect of establishing such rates via several existing information-theoretic frameworks: input-output mutual information bounds, conditional mutual information bounds and variants, PAC-Bayes bounds, and recent conditional variants thereof. We prove that none of these…

## 4 Citations

### Information Theoretic Lower Bounds for Information Theoretic Upper Bounds

- Computer ScienceArXiv
- 2023

Stochastic convex optimization reveals that, for true risk minimization, dimension-dependent mutual information is necessary and indicates that existing information-theoretic generalization bounds fall short in capturing the generalization capabilities of algorithms like SGD and regularized ERM, which have dimension-independent sample complexity.

### Exactly Tight Information-Theoretic Generalization Error Bound for the Quadratic Gaussian Problem

- Computer Science
- 2023

It is shown that although the conditional bounding and the reference distribution can make the bound exactly tight, removing them does not significantly degrade the bound, which leads to a mutual-information-based bound that is also asymptotically tight in this setting.

### Tighter Information-Theoretic Generalization Bounds from Supersamples

- Computer ScienceArXiv
- 2023

We present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke&Zakynthinou (2020)-the setting of the"conditional mutual…

### Select without Fear: Almost All Mini-Batch Schedules Generalize Optimally

- Computer ScienceArXiv
- 2023

For smooth (non-Lipschitz) nonconvex losses, it is shown that full-batch (deterministic) GD is essentially optimal, among all possible batch schedules within the considered class, including all stochastic ones.

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