1. Imitation Learning: The proposed method needs to be trained by behavioral cloning, which means 1) it requires a carefully well-designed algorithm (e.g., ODA-T/B/K) to generate the supervised data set. 2) More importantly, the data generated by ODA with a time limit L is indeed not a perfect teacher for behavioral cloning. Since all the ODAs are not designed and optimized for bounded time performance, their behavior (the state-action pairs) for the first L time is not the optimal policy under time limit L.
Since the generic algorithm procedure of ODA can be encoded as a MDP, is it possible to use reinforcement learning to train the model? Would the RL-based approach find a better policy for bounded time performance that is aware of the time limit T？
2. Performance with Different Time Limits: It seems that the proposed method is both trained and tested with a single fixed time limit T = 1000s for all problems. However, in practice, the applications could have very different run time limits. Will the proposed method generalize well to different time limits (such as 1/10/100/2000/5000s)?
3. Comparison with PMOCO: PMOCO is the only learning-based approach in the comparison, but it has a very small cardinality (feasible points) for most problems. Its approximated Pareto front is also relatively sparse (which means a small set of solutions) in Figure A.3. This result is a bit counter-intuitive.
In my understanding, PMOCO is a construction-based neural combinatorial optimization algorithm, of which one important advantage is the very fast run time. The PMOCO paper [1] reports it can generate 101 solutions for 100 MOKP(2-100) instances (hence 10,100 solutions in total) in only 15s, and 10,011 solutions for 100 MOTSP(3-100) instances (hence 1,001,100 solutions in total) in 33 minutes (~2000s). In this work, with a large time limit of 1,000s, I think POMO should be able to generate a dense set of solutions for each instance.
In addition, while a dataset with 100 instances could provide enough supervised ODA state-action pairs (with a time limit L = 1000s for each instance) for imitation learning, it is far from enough for PMOCO's RL-based training. Since PMOCO does not require any supervised data and the MOKP instances can be easily generated on the fly, is it more suitable to train PMOCO under the same wall-clock time with the proposed method?
[1] Pareto set learning for neural multi-objective combinatorial optimization. ICLR 2022.
The limitations of this work are 1) the requirement of ODAs and a well-designed IP solver; 2) it loses the guarantee for finding the whole Pareto front. They have been properly discussed in the paper (see remark at the end of Section 4.1 and Conclusion).
I do not see any potential negative societal impact of this work.
2) it loses the guarantee for finding the whole Pareto front. They have been properly discussed in the paper (see remark at the end of Section 4.1 and Conclusion). I do not see any potential negative societal impact of this work.