Guided policy search algorithms can be used to optimize complex nonlinear policies, such as deep neural networks, without directly computing policy gradients in the high-dimensional parameter space. Instead, these methods use supervised learning to train the policy to mimic a "teacher" algorithm, such as a trajectory optimizer or a trajectory-centric reinforcement learning method. Guided policy search methods provide asymptotic local convergence guarantees by construction, but it is not clear how much the policy improves within a small, finite number of iterations. We show that guided policy search algorithms can be interpreted as an approximate variant of mirror descent, where the projection onto the constraint manifold is not exact. We derive a new guided policy search algorithm that is simpler and provides appealing improvement and convergence guarantees in simplified convex and linear settings, and show that in the more general nonlinear setting, the error in the projection step can be bounded. We provide empirical results on several simulated robotic navigation and manipulation tasks that show that our method is stable and achieves similar or better performance when compared to prior guided policy search methods, with a simpler formulation and fewer hyperparameters.

First, as R4 suggested, "symbolic35 tree" was more approachable for people in the ML community. Second, the symbolic tree is declared by the user using36 decorators and serves to represent high-level program constructs, which is different from the AST that represents all37 the syntactic structures for the program. For example, the full Python AST contains information about objects' class38 methods, whereas our symbolic representation does not.39 R4: "Second, most of their tool/language design could be summarized as adding some kind of non determinis-40 tic/parametric choice ... It's extension to ML does not introduce anything particularly new ..."41 We agree with R4 that symbolic programming and non-deterministic programming are well-studied topics in the PL42 community. However, we would like to emphasize that this work is the first to introduce such concepts to AutoML43 to significantly reduce engineering effort, which is a novel and useful contribution. For example, PyGlove leverages44 symbolic manipulation to decouple the search algorithm, search space and child program, which enabled us to unify45 the interface among search methods with and without weight sharing. To enable symbolic programming in Python,46 PyGlove implements an object model for maintaining the consistency of program state during symbolic manipulation.47 R4 "Provide the grammar in the main text"48 We understand the "grammar" here as a reference to the formal definition of the search space specification. We will49 revise current Appendix Table 3 into a formal definition, and add it to the "search space" sub-section.50

We study the deterministic global optimization of the K-Medoids clustering problem. This work proposes a branch and bound (BB) scheme, in which a tailored Lagrangian relaxation method proposed in the 1970s is used to provide a lower bound at each BB node. The lower bounding method already guarantees the maximum gap at the root node. A closed-form solution to the lower bound can be derived analytically without explicitly solving any optimization problems, and its computation can be easily parallelized. Moreover, with this lower bounding method, finite convergence to the global optimal solution can be guaranteed by branching only on the regions of medoids. We also present several tailored bound tightening techniques to reduce the search space and computational cost. Extensive computational studies on 28 machine learning datasets demonstrate that our algorithm can provide a provable global optimal solution with an optimality gap of 0.1% within 4 hours on datasets with up to one million samples. Besides, our algorithm can obtain better or equal objective values than the heuristic method. A theoretical proof of global convergence for our algorithm is also presented.

Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian optimization has recently made significant progress in solving such problems, an in-depth analysis reveals that the current state-of-the-art methods are not reliable. Their performances degrade substantially when the unknown optima of the function do not have a certain structure. To fill the need for a reliable algorithm for combinatorial and mixed spaces, this paper proposes Bounce that relies on a novel map of various variable types into nested embeddings of increasing dimensionality. Comprehensive experiments show that Bounce reliably achieves and often even improves upon state-of-the-art performance on a variety of high-dimensional problems.

Automatic feature engineering is an effective approach for improving predictive performance in tabular learning. However, expand-and-reduce methods, such as OpenFE, become increasingly computationally expensive as the input dimensionality grows. This limitation arises primarily from the combinatorial explosion of candidate features generated through operator-feature combinations. To address this issue, we propose SCOPE-FE, a structured search space control framework that improves efficiency by reducing the candidate space prior to feature generation. SCOPE-FE jointly regulates two major sources of combinatorial growth: the operator space and feature-pair space. First, OperatorProbing estimates the dataset-specific utility of candidate operators and eliminates low-contribution operators in advance. Second, FeatureClustering employs spectral embedding and fuzzy c-means clustering to group structurally related features, thereby restricting candidate generation to relevant within-cluster combinations. In addition, we introduce ReliabilityScoring, which incorporates variance across subsamples to stabilize pruning decisions. Experiments on ten benchmark datasets demonstrate that SCOPE-FE substantially reduces feature engineering time while maintaining competitive predictive performance relative to existing baselines. The efficiency gains are particularly pronounced for high-dimensional datasets. These results indicate that structured control of the search space is an effective strategy for scalable automatic feature engineering. The code will be made publicly available upon acceptance.

We consider a contextual bandit problem with S contexts and K actions. In each round t = 1,2,... the learner observes a random context and chooses an action based on its past experience. The learner then observes a random reward whose mean is a function of the context and the action for the round. Under the assumption that the contexts can be lumped into r min{S,K}groups such that the mean reward for the various actions is the same for any two contexts that are in the same group, we give an algorithm that outputs an ε-optimal policy after using at most eO(r(S+K)/ε2) samples with high probability and provide a matching Ω(r(S + K)/ε2) lower bound. In the regret minimization setting, we give an algorithm whose cumulative regret up to time T is bounded by eO( p r3(S+K)T). To the best of our knowledge, we are the first to show the near-optimal sample complexity in the PAC setting and eO( p poly(r)(S+K)T)minimax regret in the online setting for this problem. We also show our algorithms can be applied to more general low-rank bandits and get improved regret bounds in some scenarios.

G.1 Monoids Monoids are one of the simplest algebraic structure.