We thank all the reviewers for their insightful comments! All the responses will be incorporated into our revision. Details of supervised learning approach: architecture embeddings and search strategies (e.g., BO) are jointly We covered some details in Supplementary A. We will add a thorough We will add this result in the revised version. We will add the discussions on [1,2] in the revised version. Thanks for suggesting the related work.

This paper considers stochastic first-order algorithms for minimax optimization under Polyak-Łojasiewicz (PL) conditions.

Mostly, if not always, these works have focussed on the task of classification or regression.

Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC) such as simulated annealing or parallel tempering, one assumes homogeneous (equilibrium) temperature profiles across input. This instance independent approach was shown to be ineffective for the hardest benchmarks near a computational phase transition when the so-called overlap-gap-property holds. In these regimes conventional MCMC struggles to unfreeze rigid variables, escape suboptimal basins of attraction, and sample high-quality and diverse solutions. In order to mitigate these challenges, Nonequilibrium Nonlocal Monte Carlo (NMC) algorithms were proposed that leverage inhomogeneous temperature profiles thereby accelerating exploration of the configuration space without compromising its exploitation. Here, we employ deep reinforcement learning (RL) to train the nonlocal transition policies of NMC which were previously designed phenomenologically. We demonstrate that the resulting solver can be trained solely by observing energy changes of the configuration space exploration as RL rewards and the local minimum energy landscape geometry as RL states. We further show that the trained policies improve upon the standard MCMC-based and nonlocal simulated annealing on hard uniform random and scale-free random 4-SAT benchmarks in terms of residual energy, time-to-solution, and diversity of solutions metrics.

The knowledge seeking procedure described in Section 2.1 applies a search algorithm over the graph Each of such queries takes constant time. As mentioned in Section 2.3, the approach described in this paper can be used to answer any valid We proceed by induction on the number of literals |Q |. 3 Base case. For the experiments on KBQA, we assume that we only have access to pairs of questions and answers, i.e. the actual inferential chain leading from the question to the answer is latent. Therefore, we resort to weak supervision to train the model. Inspired by such insight, we employ a similar technique to enhance the performance of our model.

We also generalize our results to the settings of bounded size interventions and node-dependent interventional costs. For all the above settings, we provide the first known provable algorithms for efficiently computing (near)-optimal verifying sets on general graphs.

We also generalize our results to the settings of bounded size interventions and node-dependent interventional costs. For all the above settings, we provide the first known provable algorithms for efficiently computing (near)-optimal verifying sets on general graphs.