Venue: ICLR 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: ##########################################################################
Summary:
 
The paper provides an interesting approach to speeding up the convergence time of the Policy-Space Response Oracles framework by re-using the Q-functions of past best-responses to transfer knowledge across epochs.
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Reasons for score: 
 
Overall, I am low confidence on my assessment of this paper due to the exposition in the algorithm section being relatively confusing. The experimental results are interesting which suggests that the method has value but there is key missing information on how the best response policies are constructed that make it difficult to assess the paper and lead to my not wanting to recommend its acceptance. I would highly recommend being more detailed in Sec. 3 to allow me to reassess the paper. I would certainly be willing to update my score if the paper was clearer to read.
 ##########################################################################Pros: 
 
1. The experimental results on Leduc Poker are very speedy in terms of time-steps. 

2. The idea of reusing the prior Q functions and just mixing them together rather than re-learning all of the policies is very good. 

 
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Cons: 

1. The algorithm boxes are so high level that I am struggling to understand how the algorithms work. I would not be able to implement it from reading the paper. 

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Things that would improve readability:

- It would be nice in the algorithm boxes to connect Q-mixing to how the best policy is explicitly output. I was not able to understand how Q-mixing was connected to either Algorithm 2 or 3 and subsequently had difficulty following the paper.
- \lambda does not appear to be defined anywhere but appears in the Mixed Oracles algorithm box
- What is the OpponentOracle and the TransferOracle? They are defined in the algorithm boxes but are not clearly defined elsewhere.
- The specific example of RPS in section 3.2 does not provide useful intuition by going through the numerics, it may be more helpful to walk through a more high level description. 
- It would probably be useful to move more of the experimental results to an appendix to leave room for the exposition of the algorithms.
review_title: Interesting work but exposition makes it hard to assess.

final_score: rating: 7: Good paper, accept
review_content: Summary
The paper proposes two new methods in the Policy-Space Response Oracle framework. These approaches permit to reuse past knowledge in order to reduce the amount of data required for the RL training. The first algorithm Mixed-Oracles transfers the previous iteration of Deep RL, instead of the second one, Mixed-Opponents, transfers existing strategy action-value estimates.

Strengths
The paper proposes two convincing alternatives to reuse previous knowledge in the PSRO framework. The two ideas are based on Q-mixing approach: the first one uses this method to transfer Q-values across epochs, the second one to design a new training objective. 
The experiments show that the proposed methods find a good solution using less simulation than the original PSRO framework. 

Weakness
The paper is not very novel, since it uses previous approaches (PSRO and Q-mixing) to transfer knowledge for the PSRO framework. 
I am not aware of recent works in this framework but could be useful to compare the proposed approaches with P2RO [1].
The Mixed-Opponent section needs a better explanation of the use of Q-mixing as a training objective.

[1]  McAleer, S., Lanier, J., Fox, R., & Baldi, P. (2020). Pipeline PSRO: A Scalable Approach for Finding Approximate Nash Equilibria in Large Games. arXiv preprint arXiv:2006.08555.
review_title: Review of Iterative Empirical Game Solving via Single Policy Best Response 

final_score: rating: 7: Good paper, accept
review_content: The paper focuses on resolving the computational and sample efficiency challenges with current PSRO style approaches. To this end it proposes two different modifications to the standard PSRO setup: 1) Mixed Oracles, and 2) Mixed Opponents. These approaches allow avoiding resetting learning after each outer loop epoch and reduce the stochasticity of dynamics during training. Thee efficacy is demonstrated on relatively simple games but using Deep RL policies where the proposed approaches are at least on par with standard PSRO approach in terms of final performance while drastically improving the sample efficiency.


Although the paper has quite a few typos and unclear writing in places, it has a fantastic setup with clear description of the problems with standard PSRO it's trying to resolve. The paper points out the clear computational deficiencies with current PSRO style approaches: 1) starting anew everytime, 2) slower exploration of strategy space, 3) stochastic dynamics making learning difficult.


The paper is mostly focused on two-player zero sum games.
Approach heavily dependent on efficacy of Q-mixing approach (although the idea is more general), so currently limited to discrete action problems.
Moreover, since there are no alternatives to Q-mixing, we don't actually get any understanding/intuition for why this works and how important is the performance of "TransferOracle" or "OpponentOracle".

Although section 4.4 suggests that the two stage hyperparameter selection wasn't as important, results in Fig 6b are too noisy to fully accept. It's unclear how much compute/samples were required for the hyper parameter selection. In general the results are a lot more noisier for the proposed approaches vs standard PSRO.

**Minor** 
- Environment dynamics should be SxA rather than OxA
- Algorithm 4.1 does not exist?
- Fig 1. Is it because of PSRO with Nash. Would a different MSS work differently?
- "proposes MCC as a solution concept": not everyone would know what MCC refers to. 
review_title: Important step towards efficient PSRO

final_score: rating: 7: Good paper, accept
review_content: The paper suggests two techniques to improve the calculation of empirically figuring out a Nash equilibrium using an iterative application of best-response dynamics. One method learns the best-response to the previously used strategy. The other uses that technique to model the opponent, and then best-responds to the modeled opponent. The experiments show a faster reaching to NE than without these changes.

The paper is well-written and explained, and is accessible even to researchers not well-versed in ML topics. While, the suggested changes are rather straightforward, they do indeed lead to the expected advance (shorter times to reach NE). I was convinced by further introspection that this is a significant enough contribution, to merit acceptance.

Of course, a more significant change to the algorithm, leading not only to a shorter time but to convergence to better equilibria (in cases where multiple exist) would be far more compelling.
review_title: Good ideas, but do not seem significant enough

Meta-review: This paper proposes a method to improve the convergence time of PSRO. The paper was well received by all reviewers and is likely to be of interest to a similar sub-community within ICLR, but may be of less relevance to the wider community not focused on multi-agent learning. 

A number of issues were raised by reviewers regarding the clarity of the originally submitted version of the paper. I encourage the authors to consider all constructive feedback given and revise the paper to maximise its impact. This will be of particular help in reaching a wider audience than those with pre-existing experience with the methods this work builds on.
Decision: Accept (Spotlight)