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Register a new userOnline Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization
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Added by
Fransisca Susan
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Rad Niazadeh
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Motivated by online decision-making in time-varying combinatorial environments, we study the problem of transforming offline algorithms to their online counterparts. We focus on offline combinatorial problems that are amenable to a constant factor approximation using a greedy algorithm that is robust to local errors. For such problems, we provide a general framework that efficiently transforms offline robust greedy algorithms to online ones using Blackwell approachability. We show that the resulting online algorithms have $O(sqrt{T})$ (approximate) regret under the full information setting. We further introduce a bandit extension of Blackwell approachability that we call Bandit Blackwell approachability. We leverage this notion to transform greedy robust offline algorithms into a $O(T^{2/3})$ (approximate) regret in the bandit setting. Demonstrating the flexibility of our framework, we apply our offline-to-online transformation to several problems at the intersection of revenue management, market design, and online optimization, including product ranking optimization in online platforms, reserve price optimization in auctions, and submodular maximization. We show that our transformation, when applied to these applications, leads to new regret bounds or improves the current known bounds.
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We present a general, efficient technique for providing contextual predictions that are multivalid in various senses, against an online sequence of adversarially chosen examples $(x,y)$. This means that the resulting estimates correctly predict various statistics of the labels $y$ not just marginally -- as averaged over the sequence of examples -- but also conditionally on $x in G$ for any $G$ belonging to an arbitrary intersecting collection of groups $mathcal{G}$. We provide three instantiations of this framework. The first is mean prediction, which corresponds to an online algorithm satisfying the notion of multicalibration from Hebert-Johnson et al. The second is variance and higher moment prediction, which corresponds to an online algorithm satisfying the notion of mean-conditioned moment multicalibration from Jung et al. Finally, we define a new notion of prediction interval multivalidity, and give an algorithm for finding prediction intervals which satisfy it. Because our algorithms handle adversarially chosen examples, they can equally well be used to predict statistics of the residuals of arbitrary point prediction methods, giving rise to very general techniques for quantifying the uncertainty of predictions of black box algorithms, even in an online adversarial setting. When instantiated for prediction intervals, this solves a similar problem as conformal prediction, but in an adversarial environment and with multivalidity guarantees stronger than simple marginal coverage guarantees.
Motivated by the use of high speed circuit switches in large scale data centers, we consider the problem of circuit switch scheduling. In this problem we are given demands between pairs of servers and the goal is to schedule at every time step a matching between the servers while maximizing the total satisfied demand over time. The crux of this scheduling problem is that once one shifts from one matching to a different one a fixed delay $delta$ is incurred during which no data can be transmitted. For the offline version of the problem we present a $(1-frac{1}{e}-epsilon)$ approximation ratio (for any constant $epsilon >0$). Since the natural linear programming relaxation for the problem has an unbounded integrality gap, we adopt a hybrid approach that combines the combinatorial greedy with randomized rounding of a different suitable linear program. For the online version of the problem we present a (bi-criteria) $ ((e-1)/(2e-1)-epsilon)$-competitive ratio (for any constant $epsilon >0$ ) that exceeds time by an additive factor of $O(frac{delta}{epsilon})$. We note that no uni-criteria online algorithm is possible. Surprisingly, we obtain the result by reducing the online version to the offline one.
We consider a variation on the classical finance problem of optimal portfolio design. In our setting, a large population of consumers is drawn from some distribution over risk tolerances, and each consumer must be assigned to a portfolio of lower risk than her tolerance. The consumers may also belong to underlying groups (for instance, of demographic properties or wealth), and the goal is to design a small number of portfolios that are fair across groups in a particular and natural technical sense. Our main results are algorithms for optimal and near-optimal portfolio design for both social welfare and fairness objectives, both with and without assumptions on the underlying group structure. We describe an efficient algorithm based on an internal two-player zero-sum game that learns near-optimal fair portfolios ex ante and show experimentally that it can be used to obtain a small set of fair portfolios ex post as well. For the special but natural case in which group structure coincides with risk tolerances (which models the reality that wealthy consumers generally tolerate greater risk), we give an efficient and optimal fair algorithm. We also provide generalization guarantees for the underlying risk distribution that has no dependence on the number of portfolios and illustrate the theory with simulation results.
This paper leverages machine-learned predictions to design competitive algorithms for online conversion problems with the goal of improving the competitive ratio when predictions are accurate (i.e., consistency), while also guaranteeing a worst-case competitive ratio regardless of the prediction quality (i.e., robustness). We unify the algorithmic design of both integral and fractional conversion problems, which are also known as the 1-max-search and one-way trading problems, into a class of online threshold-based algorithms (OTA). By incorporating predictions into design of OTA, we achieve the Pareto-optimal trade-off of consistency and robustness, i.e., no online algorithm can achieve a better consistency guarantee given for a robustness guarantee. We demonstrate the performance of OTA using numerical experiments on Bitcoin conversion.
Most reinforcement learning (RL) algorithms assume online access to the environment, in which one may readily interleave updates to the policy with experience collection using that policy. However, in many real-world applications such as health, education, dialogue agents, and robotics, the cost or potential risk of deploying a new data-collection policy is high, to the point that it can become prohibitive to update the data-collection policy more than a few times during learning. With this view, we propose a novel concept of deployment efficiency, measuring the number of distinct data-collection policies that are used during policy learning. We observe that na{i}vely applying existing model-free offline RL algorithms recursively does not lead to a practical deployment-efficient and sample-efficient algorithm. We propose a novel model-based algorithm, Behavior-Regularized Model-ENsemble (BREMEN) that can effectively optimize a policy offline using 10-20 times fewer data than prior works. Furthermore, the recursive application of BREMEN is able to achieve impressive deployment efficiency while maintaining the same or better sample efficiency, learning successful policies from scratch on simulated robotic environments with only 5-10 deployments, compared to typical values of hundreds to millions in standard RL baselines. Codes and pre-trained models are available at https://github.com/matsuolab/BREMEN .
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