The ability to identify and acquire missing information is a critical component of effective decision making and problem solving. With the rise of conversational artificial intelligence (AI) systems, strategically formulating information-seeking questions becomes crucial and demands efficient methods to guide the search process. We introduce a novel approach to adaptive question-asking through a combination of Large Language Models (LLM) for generating questions that maximize information gain, Monte Carlo Tree Search (MCTS) for constructing and leveraging a decision tree across multiple samples, and a hierarchical feedback mechanism to learn from past interactions. We present two key innovations: (1) an adaptive MCTS algorithm that balances exploration and exploitation for efficient search over potential questions; and (2) a clustering-based feedback algorithm that leverages prior experience to guide future interactions. Each incoming sample is assigned to a cluster based on its semantic similarity with previously observed samples. Our UCT (Upper Confidence bound for Trees) formulation selects optimal questions by combining expected rewards, a function of information gain, with a cluster-specific bonus that decays with depth, to emphasize the importance of early-stage questions that have proven effective for narrowing the solution space in similar samples. Experiments across three domains, including medical diagnosis and troubleshooting, demonstrate that our method leads to an average of 12% improvement in success rates and a 10x reduction in the average number of LLM calls made per conversation for the search process, in comparison to the state of the art.

Efficient surgery room scheduling is essential for hospital efficiency, patient satisfaction, and resource utilization. This study addresses this challenge by introducing a novel concept of Random-Key Optimizer (RKO), rigorously tested on literature and new, real-world inspired instances. Our combinatorial optimization problem incorporates multi-room scheduling, equipment scheduling, and complex availability constraints for rooms, patients, and surgeons, facilitating rescheduling and enhancing operational flexibility. The RKO approach represents solutions as points in a continuous space, which are then mapped in the problem solution space via a deterministic function known as a decoder. The core idea is to operate metaheuristics and heuristics in the random-key space, unaware of the original solution space. We design the Biased Random-Key Genetic Algorithm with $Q$-Learning, Simulated Annealing, and Iterated Local Search for use within an RKO framework, employing a single decoder function. The proposed metaheuristics are complemented by lower-bound formulations, providing optimal gaps for evaluating the effectiveness of the heuristic results. Our results demonstrate significant lower and upper bounds improvements for the literature instances, notably proving one optimal result. Furthermore, the best-proposed metaheuristic efficiently generates schedules for the newly introduced instances, even in highly constrained scenarios. This research offers valuable insights and practical solutions for improving surgery scheduling processes, offering tangible benefits to hospitals by optimising resource allocation, reducing patient wait times, and enhancing overall operational efficiency.

Additional Feedback: Questions in random ordering: - Would it be possible to provide dependences on the diameter(s) D_Y (and D_X?) in Table 1? - Reference for point (ii) page 3? - line 147: although this additional evaluation is certainly "negligible" for deterministic methods, is it really the case for stochastic ones? Was this cost taken into account in the numerical experiments? I guess there should be no gain (due to lower bound & EG), but e.g., do we also lose the logarithmic factor? If not, please make it more explicit (e.g., in the abstract; "state-of-the-art" makes it a bit implicit) To go further: - Is it possible to use the method with raw estimates of mu and/or l? - (lines 42-54): Given that there is no known optimal algorithm; is it possible that the lower bound is not tight? In particular, in the abstract, the word "first" is probably a bit abusive, given that there exists closely related methods for closely related settings (e.g., [40]).

The paper received positive feedback. After reading the rebuttal and discussing the paper, the general consensus is that the paper should be accepted. The area chair agrees with this assessement and follows the reviewer's recommendation. Several suggestions were made to improve the paper (see in particular R1's review), which will be good to take into account for the final version.

This paper proposes a formal langauge to describe the search space of architecture search problem. This langauge is a domain specific language embedded in python. Users can write modular, composable, and reusable search space by using this langauge. Originality: The contribution is new. This is the first work that tries to provide a formal langauge for the space definition.

Summary and Contributions: This work considers the problem of synthesizing programs from input/outputs, but where some of the components of the program might have continuous parameters, and where the entire program is differentiable with respect to these parameters. Neurosymbolic programs are a special case of this set up (symbolic programs which can call out to neural modules if needed). This is an especially challenging combinatorial search problem, because not only do we have to consider an infinitely large, discrete space of program structures, but we also have to consider an inner-loop optimization over continuous parameters. The approach they take is to perform an explicit symbolic graph search over the discrete space of partial programs. As a heuristic function for this graph search, they train neural networks to approximate the behavior of incomplete portions of the program syntax tree.

Weaknesses: Although I believe the math derivation of the novel minimax objective function is correct, I have two major concerns. My first concern is whether this minimax objective function provides some novel insight on network dynamics which cannot be captured by traditional framework that network dynamics is minimizing an "energy" function. My concern is resulted from that the minimax objective (Eq. It seems to me that the only difference between the minimax and minimized objective function is that the network state converges to the saddle point in the former case, while in later case the network state converges to a stable fixed point. I really hope the authors explain this and correct me if I understood something wrong.

The reviewers were originally divergent in their opinions of this paper, but came to some agreements in discussion. It was agreed that the paper provides an interesting contribution for neuroscience by extending the previous work of Seung et al. (1997) to more biologically realistic networks, but the actual theoretical insights beyond that original paper are not large. In the end, an "accept" decision was reached, but it was agreed that the authors should better clarify the strong links to the Seung paper and be more cautious in their claims of "detailed" or "tight" balance in cortical networks.

Relation to Prior Work: In addition to the papers mentioned above, the relation to the literature of monotone VI should be discussed in details. The convex-concave min-max falls into the category of monotone VIs and there are many works in the literature addressing that. For example, the following papers should be discussed: Ronald E Bruck Jr. Dual extrapolation and its applications to solving variational inequalities and related problems. Solving variational inequalities with monotone operators on domains given by linear minimization oracles.

Authors propose a novel algorithm that achieves linear convergence rate and improved dependence on the condition numbers, compared to prior work.