The feedback arc set problem is one of the most fundamental and well-studied ranking problems where n objects are to be ordered based on their pairwise comparison. The problem enjoys several efficient approximation algorithms in the offline setting. Unfortunately, online there are strong lower bounds on the competitive ratio establishing that no algorithm can perform well in the worst case.This paper introduces a new beyond-worst-case model for online feedback arc set. In the model, a sample of the input is given to the algorithm offline before the remaining instance is revealed online. This models the case in practice where yesterday's data is available and is similar to today's online instance. This sample is drawn from a known distribution which may not be uniform. We design an online algorithm with strong theoretical guarantees. The algorithm has a small constant competitive ratio when the sample is uniform---if not, we show we can recover the same result by adding a provably minimal sample. Empirical results validate the theory and show that such algorithms can be used on temporal data to obtain strong results.
Data-driven Competitive Algorithms for Online Knapsack and Set Cover
The design of online algorithms has tended to focus on algorithms with worst-case guarantees, e.g., bounds on the competitive ratio. However, it is well-known that such algorithms are often overly pessimistic, performing sub-optimally on non-worst-case inputs. In this paper, we develop an approach for data-driven design of online algorithms that maintain near-optimal worst-case guarantees while also performing learning in order to perform well for typical inputs. Our approach is to identify policy classes that admit global worst-case guarantees, and then perform learning using historical data within the policy classes. We demonstrate the approach in the context of two classical problems, online knapsack, and online set cover, proving competitive bounds for rich policy classes in each case. Additionally, we illustrate the practical implications via a case study on electric vehicle charging.
more »
« less
- Award ID(s):
- 1908298
- PAR ID:
- 10296204
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- ISSN:
- 2159-5399
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
-
This paper considers the recently popular beyond-worst-case algorithm analysis model which integrates machine-learned predictions with online algorithm design. We consider the online Steiner tree problem in this model for both directed and undirected graphs. Steiner tree is known to have strong lower bounds in the online setting and any algorithm’s worst-case guarantee is far from desirable. This paper considers algorithms that predict which terminal arrives online. The predictions may be incorrect and the algorithms’ performance is parameterized by the number of incorrectly predicted terminals. These guarantees ensure that algorithms break through the online lower bounds with good predictions and the competitive ratio gracefully degrades as the prediction error grows. We then observe that the theory is predictive of what will occur empirically. We show on graphs where terminals are drawn from a distribution, the new online algorithms have strong performance even with modestly correct predictions.more » « less
-
Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert’s decision or the RL decision for each online item. We prove that for any rho in [0,1], LOMAR is rho-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines.more » « less
-
The online knapsack problem is a classic online resource allocation problem in networking and operations research. Its basic version studies how to pack online arriving items of different sizes and values into a capacity-limited knapsack. In this paper, we study a general version that includes item departures, while also considering multiple knapsacks and multi-dimensional item sizes. We design a threshold-based online algorithm and prove that the algorithm can achieve order-optimal competitive ratios. Beyond worst-case performance guarantees, we also aim to achieve near-optimal average performance under typical instances. Towards this goal, we propose a data-driven online algorithm that learns within a policy-class that guarantees a worst-case performance bound. In trace-driven experiments, we show that our data-driven algorithm outperforms other benchmark algorithms in an application of online knapsack to job scheduling for cloud computing.more » « less
-
We devise an online learning algorithm -- titled Switching via Monotone Adapted Regret Traces (SMART) -- that adapts to the data and achieves regret that is instance optimal, i.e., simultaneously competitive on every input sequence compared to the performance of the follow-the-leader (FTL) policy and the worst case guarantee of any other input policy. We show that the regret of the SMART policy on any input sequence is within a multiplicative factor e/(e−1)≈1.58 of the smaller of: 1) the regret obtained by FTL on the sequence, and 2) the upper bound on regret guaranteed by the given worst-case policy. This implies a strictly stronger guarantee than typical `best-of-both-worlds' bounds as the guarantee holds for every input sequence regardless of how it is generated. SMART is simple to implement as it begins by playing FTL and switches at most once during the time horizon to the worst-case algorithm. Our approach and results follow from an operational reduction of instance optimal online learning to competitive analysis for the ski-rental problem. We complement our competitive ratio upper bounds with a fundamental lower bound showing that over all input sequences, no algorithm can get better than a 1.43-fraction of the minimum regret achieved by FTL and the minimax-optimal policy. We also present a modification of SMART that combines FTL with a ``small-loss" algorithm to achieve instance optimality between the regret of FTL and the small loss regret bound.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
