Online Optimization with Untrusted Predictions

• URL: http://arxiv.org/abs/2202.03519v1
• Date: Mon, 7 Feb 2022 21:08:02 GMT
• Title: Online Optimization with Untrusted Predictions
• Authors: Daan Rutten, Nico Christianson, Debankur Mukherjee, Adam Wierman
• Abstract summary: We study the problem of online optimization, where a decision maker must choose points in a general metric space to the sum of per-round, non-competitive hitting costs and the costs of switching between rounds. We propose a novel algorithm, Adaptive Online Switching (AOS), and prove that, for any desired $delta 0)$competitive if predictions are perfect, it is $tildecalO(alphadelta)$ even when predictions are inaccurate.
• Score: 7.895232155155041
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine the problem of online optimization, where a decision maker must sequentially choose points in a general metric space to minimize the sum of per-round, non-convex hitting costs and the costs of switching decisions between rounds. The decision maker has access to a black-box oracle, such as a machine learning model, that provides untrusted and potentially inaccurate predictions of the optimal decision in each round. The goal of the decision maker is to exploit the predictions if they are accurate, while guaranteeing performance that is not much worse than the hindsight optimal sequence of decisions, even when predictions are inaccurate. We impose the standard assumption that hitting costs are globally $\alpha$-polyhedral. We propose a novel algorithm, Adaptive Online Switching (AOS), and prove that, for any desired $\delta > 0$, it is $(1+2\delta)$-competitive if predictions are perfect, while also maintaining a uniformly bounded competitive ratio of $2^{\tilde{\mathcal{O}}(1/(\alpha \delta))}$ even when predictions are adversarial. Further, we prove that this trade-off is necessary and nearly optimal in the sense that any deterministic algorithm which is $(1+\delta)$-competitive if predictions are perfect must be at least $2^{\tilde{\Omega}(1/(\alpha \delta))}$-competitive when predictions are inaccurate.

Related papers

• Mind the Gap: A Causal Perspective on Bias Amplification in Prediction & Decision-Making [58.06306331390586]
  We introduce the notion of a margin complement, which measures how much a prediction score $S$ changes due to a thresholding operation. We show that under suitable causal assumptions, the influences of $X$ on the prediction score $S$ are equal to the influences of $X$ on the true outcome $Y$.
  arXiv  Detail & Related papers  (2024-05-24T11:22:19Z)
• Competitive strategies to use "warm start" algorithms with predictions [12.970501425097645]
  We consider the problem of learning and using predictions for warm start algorithms with predictions. In this setting, an algorithm is given an instance of a problem, and a prediction of the solution. We give competitive guarantees against stronger benchmarks that consider a set of $k$ predictions.
  arXiv  Detail & Related papers  (2024-05-06T17:38:20Z)
• Sorting and Hypergraph Orientation under Uncertainty with Predictions [0.45880283710344055]
  We study learning-augmented algorithms for sorting and hypergraph orientation under uncertainty. Our algorithms provide improved performance guarantees for accurate predictions while maintaining worst-case guarantees that are best possible without predictions.
  arXiv  Detail & Related papers  (2023-05-16T07:52:08Z)
• Mixing predictions for online metric algorithms [34.849039387367455]
  We design algorithms that combine predictions and are competitive against such dynamic combinations. Our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the $k$-server problem.
  arXiv  Detail & Related papers  (2023-04-04T13:18:00Z)
• Streaming Algorithms for Learning with Experts: Deterministic Versus Robust [62.98860182111096]
  In the online learning with experts problem, an algorithm must make a prediction about an outcome on each of $T$ days (or times) The goal is to make a prediction with the minimum cost, specifically compared to the best expert in the set. We show a space lower bound of $widetildeOmegaleft(fracnMRTright)$ for any deterministic algorithm that achieves regret $R$ when the best expert makes $M$ mistakes.
  arXiv  Detail & Related papers  (2023-03-03T04:39:53Z)
• Autoregressive Bandits [58.46584210388307]
  We propose a novel online learning setting, Autoregressive Bandits, in which the observed reward is governed by an autoregressive process of order $k$. We show that, under mild assumptions on the reward process, the optimal policy can be conveniently computed. We then devise a new optimistic regret minimization algorithm, namely, AutoRegressive Upper Confidence Bound (AR-UCB), that suffers sublinear regret of order $widetildemathcalO left( frac(k+1)3/2sqrtnT (1-G
  arXiv  Detail & Related papers  (2022-12-12T21:37:36Z)
• Learning-Augmented Algorithms for Online TSP on the Line [4.636538620253008]
  We study the online Traveling Salesman Problem (TSP) on the line augmented with machine-learned predictions. In the classical problem, there is a stream of requests released over time along the real line. We distinguish between the open variant and the closed one, in which we additionally require the algorithm to return to the origin after serving all requests.
  arXiv  Detail & Related papers  (2022-06-01T17:47:26Z)
• Revisiting Smoothed Online Learning [70.09792747315323]
  We investigate the problem of smoothed online learning, in which the online learner suffers both a hitting cost and a switching cost. To bound the competitive ratio, we assume the hitting cost is known to the learner in each round, and investigate the greedy algorithm which simply minimizes the weighted sum of the hitting cost and the switching cost.
  arXiv  Detail & Related papers  (2021-02-13T14:15:55Z)
• Almost Tight L0-norm Certified Robustness of Top-k Predictions against Adversarial Perturbations [78.23408201652984]
  Top-k predictions are used in many real-world applications such as machine learning as a service, recommender systems, and web searches. Our work is based on randomized smoothing, which builds a provably robust classifier via randomizing an input. For instance, our method can build a classifier that achieves a certified top-3 accuracy of 69.2% on ImageNet when an attacker can arbitrarily perturb 5 pixels of a testing image.
  arXiv  Detail & Related papers  (2020-11-15T21:34:44Z)
• Online Page Migration with ML Advice [26.929268665630342]
  We consider online algorithms for the em page migration problem that use predictions, potentially imperfect, to improve their performance. We show that if the algorithm is given a prediction of the input sequence, then it can achieve a competitive ratio that tends to $1$. Our result adds to the recent body of work that uses machine learning to improve the performance of classic'' algorithms.
  arXiv  Detail & Related papers  (2020-06-09T03:15:34Z)
• Toward Optimal Adversarial Policies in the Multiplicative Learning System with a Malicious Expert [87.12201611818698]
  We consider a learning system that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the system. We show that a simple greedy policy of always reporting false prediction is optimal with an approximation ratio of $1+O(sqrtfracln NN)$. For the online setting where the malicious expert can adaptively make its decisions, we show that the optimal online policy can be efficiently computed by solving a dynamic program in $O(N3)$.
  arXiv  Detail & Related papers  (2020-01-02T18:04:46Z)

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.