On-Demand Sampling: Learning Optimally from Multiple Distributions

• URL: http://arxiv.org/abs/2210.12529v3
• Date: Tue, 2 Apr 2024 22:48:13 GMT
• Title: On-Demand Sampling: Learning Optimally from Multiple Distributions
• Authors: Nika Haghtalab, Michael I. Jordan, Eric Zhao,
• Abstract summary: Social and real-world considerations have given rise to multi-distribution learning paradigms. We establish the optimal sample complexity of these learning paradigms and give algorithms that meet this sample complexity. Our algorithm design and analysis are enabled by our extensions of online learning techniques for solving zero-sum games.
• Score: 63.20009081099896
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust optimization, and fair federated learning. In each of these settings, a learner seeks to uniformly minimize its expected loss over $n$ predefined data distributions, while using as few samples as possible. In this paper, we establish the optimal sample complexity of these learning paradigms and give algorithms that meet this sample complexity. Importantly, our sample complexity bounds for multi-distribution learning exceed that of learning a single distribution by only an additive factor of $n \log(n) / \epsilon^2$. This improves upon the best known sample complexity bounds for fair federated learning by Mohri et al. and collaborative learning by Nguyen and Zakynthinou by multiplicative factors of $n$ and $\log(n)/\epsilon^3$, respectively. We also provide the first sample complexity bounds for the group DRO objective of Sagawa et al. To guarantee these optimal sample complexity bounds, our algorithms learn to sample from data distributions on demand. Our algorithm design and analysis are enabled by our extensions of online learning techniques for solving stochastic zero-sum games. In particular, we contribute stochastic variants of no-regret dynamics that can trade off between players' differing sampling costs.

Related papers

• Collaborative Learning with Different Labeling Functions [7.228285747845779]
  We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions. We show that, when the data distributions satisfy a weaker realizability assumption, sample-efficient learning is still feasible.
  arXiv  Detail & Related papers  (2024-02-16T04:32:22Z)
• Optimal Multi-Distribution Learning [88.3008613028333]
  Multi-distribution learning seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions. We propose a novel algorithm that yields an varepsilon-optimal randomized hypothesis with a sample complexity on the order of (d+k)/varepsilon2.
  arXiv  Detail & Related papers  (2023-12-08T16:06:29Z)
• Information-Computation Tradeoffs for Learning Margin Halfspaces with Random Classification Noise [50.64137465792738]
  We study the problem of PAC $gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoff suggesting an inherent gap between the sample complexity of the problem and the sample complexity of computationally efficient algorithms.
  arXiv  Detail & Related papers  (2023-06-28T16:33:39Z)
• Stochastic Approximation Approaches to Group Distributionally Robust Optimization and Beyond [89.72693227960274]
  This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. To reduce the number of samples in each round from $m$ to 1, we cast GDRO as a two-player game, where one player conducts and the other executes an online algorithm for non-oblivious multi-armed bandits. In the second scenario, we propose to optimize the average top-$k$ risk instead of the maximum risk, thereby mitigating the impact of distributions.
  arXiv  Detail & Related papers  (2023-02-18T09:24:15Z)
• Sample Complexity Bounds for Robustly Learning Decision Lists against Evasion Attacks [25.832511407411637]
  A fundamental problem in adversarial machine learning is to quantify how much training data is needed in the presence of evasion attacks. We work with probability distributions on the input data that satisfy a Lipschitz condition: nearby points have similar probability. For every fixed $k$ the class of $k$-decision lists has sample complexity against a $log(n)$-bounded adversary.
  arXiv  Detail & Related papers  (2022-05-12T14:40:18Z)
• The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model [11.821892196198457]
  We show that the sample complexity of learning $d$-bit parity functions is $Omega (2d/2)$. We also sketch a simple shuffle model protocol demonstrating that our results are tight up to $poly(d)$ factors.
  arXiv  Detail & Related papers  (2021-03-29T15:26:02Z)
• Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity [67.02490430380415]
  We show that model-based MARL achieves a sample complexity of $tilde O(|S||B|(gamma)-3epsilon-2)$ for finding the Nash equilibrium (NE) value up to some $epsilon$ error. We also show that such a sample bound is minimax-optimal (up to logarithmic factors) if the algorithm is reward-agnostic, where the algorithm queries state transition samples without reward knowledge.
  arXiv  Detail & Related papers  (2020-07-15T03:25:24Z)
• A Provably Efficient Sample Collection Strategy for Reinforcement Learning [123.69175280309226]
  One of the challenges in online reinforcement learning (RL) is that the agent needs to trade off the exploration of the environment and the exploitation of the samples to optimize its behavior. We propose to tackle the exploration-exploitation problem following a decoupled approach composed of: 1) An "objective-specific" algorithm that prescribes how many samples to collect at which states, as if it has access to a generative model (i.e., sparse simulator of the environment); 2) An "objective-agnostic" sample collection responsible for generating the prescribed samples as fast as possible.
  arXiv  Detail & Related papers  (2020-07-13T15:17:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.