YaoGAN: Learning Worst-case Competitive Algorithms from Self-generated Inputs
We tackle the challenge of using machine learning to find algorithms with strong worst-case guarantees for online combinatorial optimization problems. Whereas the previous approach along this direction (Kong et al., 2018) relies on significant domain expertise to provide hard distributions over input instances at training, we ask whether this can be accomplished from first principles, i.e., without any human-provided data beyond specifying the objective of the optimization problem. To answer this question, we draw insights from classic results in game theory, analysis of algorithms, and online learning to introduce a novel framework. At the high level, similar to a generative adversarial network (GAN), our framework has two components whose respective goals are to learn the optimal algorithm as well as a set of input instances that captures the essential difficulty of the given optimization problem. The two components are trained against each other and evolved simultaneously. We test our ideas on the ski rental problem and the fractional AdWords problem. For these well-studied problems, our preliminary results demonstrate that the framework is capable of finding algorithms as well as difficult input instances that are consistent with known optimal results. We believe our new framework points to a promising direction which can facilitate the research of algorithm design by leveraging ML to improve the state of the art both in theory and in practice.
This paper introduces a new approach to solve optimization problems without relying on any human-provided data beyond the specification of the optimization problem itself. The approach is inspired by the two-player zero-sum game paradigm and follow a generative adversarial network (GAN) setting. One network is trained to output the optimal behavior for a given problem, while the other is trained to output difficult instances of the given problem. These two networks are trained simultaneously and compete against the other until some equilibrium is achieved. This approach is tested on two small problems for which the optimal behavior is known and seems to perform near theoretical optimality. I weakly reject this paper because although the approach is indeed interesting, the paper is lacking some structure, as described below: - The paper clearly mentions that no optimization of the training setup or the hyperparameters has been done because the authors are not interested in extending ML techniques. However, hyperparameter searching is not extending any ML technique, it is just an approach to find a good training configuration and show robustness in different hyperparameters settings. It is thus unclear if the approach is robust against different hyperparameter settings. - Very little details (apart from the optimization algorithm) are given regarding the architecture used (types of input, output, neural units, activation functions, number of hidden layers, loss function, etc...), which makes it very hard to reproduce this approach. - Section 1.1 presents results with too many details without introducing the problem. I would suggest the authors to either introduce the two problems earlier or to simply say that near-optimal results are achieved, without giving detailed results, because it is very hard to understand them without any introduction of the task being achieved. - One task is presented in Section 2 *Preliminaries* while the other task is presented in Section 4 *AdWords*. It is hard to follow the flow of ideas present in the paper when similar things are not together. I would suggest restructuring the paper into a more classical structure such as: <intro without detailed results - previous work & problematic - approach taken with more details for reproducibility - description of the two tasks - description of experiments with more details for reproducibility - results - conclusion>. - The paper mentions the MSVV algorithm twice but no reference or explanation is provided. It is very hard to understand sentences referring to this. - This work only considers problems for which the optimal input distribution is known, but is motivated by the fact that it could be applied to problems for which the optimal distribution is unknown and thus being able to discover new algorithms. It is hard to support this motivation when no experiments are done in its favor. - No comparison has been made between their approach and other previous approaches. We only know that the proposed approach finds near-optimal solutions with a difference of 0.01 competitive ratio. It is thus very hard to know if this new approach brings any improvement to previous work. Below are a few things that were not considered to make a decision, but are only details that would make the paper slightly better: - typo at the beginning of section 3.1: missing *be* in *This can either *be* by an ...* - typo at the beginning os section 4: missing *be* in *... the algorithm must irrevocably *be* allocated to ...* - Axis* names to the different plots in the Figures would help understand them better. Also, the description of some figures could benefit more details that could be taken off from the text.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
YaoGAN: Learning Worst-case Competitive Algorithms from Self-generated Inputs
We tackle the challenge of using machine learning to find algorithms with strong worst-case guarantees for online combinatorial optimization problems. Whereas the previous approach along this direction (Kong et al., 2018) relies on significant domain expertise to provide hard distributions over input instances at training, we ask whether this can be accomplished from first principles, i.e., without any human-provided data beyond specifying the objective of the optimization problem. To answer this question, we draw insights from classic results in game theory, analysis of algorithms, and online learning to introduce a novel framework. At the high level, similar to a generative adversarial network (GAN), our framework has two components whose respective goals are to learn the optimal algorithm as well as a set of input instances that captures the essential difficulty of the given optimization problem. The two components are trained against each other and evolved simultaneously. We test our ideas on the ski rental problem and the fractional AdWords problem. For these well-studied problems, our preliminary results demonstrate that the framework is capable of finding algorithms as well as difficult input instances that are consistent with known optimal results. We believe our new framework points to a promising direction which can facilitate the research of algorithm design by leveraging ML to improve the state of the art both in theory and in practice.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper introduces a new approach to solve optimization problems without relying on any human-provided data beyond the specification of the optimization problem itself. The approach is inspired by the two-player zero-sum game paradigm and follow a generative adversarial network (GAN) setting. One network is trained to output the optimal behavior for a given problem, while the other is trained to output difficult instances of the given problem. These two networks are trained simultaneously and compete against the other until some equilibrium is achieved. This approach is tested on two small problems for which the optimal behavior is known and seems to perform near theoretical optimality. I weakly reject this paper because although the approach is indeed interesting, the paper is lacking some structure, as described below: - The paper clearly mentions that no optimization of the training setup or the hyperparameters has been done because the authors are not interested in extending ML techniques. However, hyperparameter searching is not extending any ML technique, it is just an approach to find a good training configuration and show robustness in different hyperparameters settings. It is thus unclear if the approach is robust against different hyperparameter settings. - Very little details (apart from the optimization algorithm) are given regarding the architecture used (types of input, output, neural units, activation functions, number of hidden layers, loss function, etc...), which makes it very hard to reproduce this approach. - Section 1.1 presents results with too many details without introducing the problem. I would suggest the authors to either introduce the two problems earlier or to simply say that near-optimal results are achieved, without giving detailed results, because it is very hard to understand them without any introduction of the task being achieved. - One task is presented in Section 2 *Preliminaries* while the other task is presented in Section 4 *AdWords*. It is hard to follow the flow of ideas present in the paper when similar things are not together. I would suggest restructuring the paper into a more classical structure such as: <intro without detailed results - previous work & problematic - approach taken with more details for reproducibility - description of the two tasks - description of experiments with more details for reproducibility - results - conclusion>. - The paper mentions the MSVV algorithm twice but no reference or explanation is provided. It is very hard to understand sentences referring to this. - This work only considers problems for which the optimal input distribution is known, but is motivated by the fact that it could be applied to problems for which the optimal distribution is unknown and thus being able to discover new algorithms. It is hard to support this motivation when no experiments are done in its favor. - No comparison has been made between their approach and other previous approaches. We only know that the proposed approach finds near-optimal solutions with a difference of 0.01 competitive ratio. It is thus very hard to know if this new approach brings any improvement to previous work. Below are a few things that were not considered to make a decision, but are only details that would make the paper slightly better: - typo at the beginning of section 3.1: missing *be* in *This can either *be* by an ...* - typo at the beginning os section 4: missing *be* in *... the algorithm must irrevocably *be* allocated to ...* - Axis* names to the different plots in the Figures would help understand them better. Also, the description of some figures could benefit more details that could be taken off from the text.
assistant
This paper introduces a new approach to solve optimization problems without relying on any human-provided data beyond the specification of the optimization problem itself. The approach is inspired by the two-player zero-sum game paradigm and follow a generative adversarial network (GAN) setting. One network is trained to output the optimal behavior for a given problem, while the other is trained to output difficult instances of the given problem. These two networks are trained simultaneously and compete against the other until some equilibrium is achieved. This approach is tested on two small problems for which the optimal behavior is known and seems to perform near theoretical optimality. I weakly reject this paper because although the approach is indeed interesting, the paper is lacking some structure, as described below: - The paper clearly mentions that no optimization of the training setup or the hyperparameters has been done because the authors are not interested in extending ML techniques. However, hyperparameter searching is not extending any ML technique, it is just an approach to find a good training configuration and show robustness in different hyperparameters settings. It is thus unclear if the approach is robust against different hyperparameter settings. - Very little details (apart from the optimization algorithm) are given regarding the architecture used (types of input, output, neural units, activation functions, number of hidden layers, loss function, etc...), which makes it very hard to reproduce this approach. - Section 1.1 presents results with too many details without introducing the problem. I would suggest the authors to either introduce the two problems earlier or to simply say that near-optimal results are achieved, without giving detailed results, because it is very hard to understand them without any introduction of the task being achieved. - One task is presented in Section 2 *Preliminaries* while the other task is presented in Section 4 *AdWords*. It is hard to follow the flow of ideas present in the paper when similar things are not together. I would suggest restructuring the paper into a more classical structure such as: <intro without detailed results - previous work & problematic - approach taken with more details for reproducibility - description of the two tasks - description of experiments with more details for reproducibility - results - conclusion>. - The paper mentions the MSVV algorithm twice but no reference or explanation is provided. It is very hard to understand sentences referring to this. - This work only considers problems for which the optimal input distribution is known, but is motivated by the fact that it could be applied to problems for which the optimal distribution is unknown and thus being able to discover new algorithms. It is hard to support this motivation when no experiments are done in its favor. - No comparison has been made between their approach and other previous approaches. We only know that the proposed approach finds near-optimal solutions with a difference of 0.01 competitive ratio. It is thus very hard to know if this new approach brings any improvement to previous work. Below are a few things that were not considered to make a decision, but are only details that would make the paper slightly better: - typo at the beginning of section 3.1: missing *be* in *This can either *be* by an ...* - typo at the beginning os section 4: missing *be* in *... the algorithm must irrevocably *be* allocated to ...* - Axis* names to the different plots in the Figures would help understand them better. Also, the description of some figures could benefit more details that could be taken off from the text.