ICML 2023 Papers

Answering complex logical queries on incomplete knowledge graphs is a challenging task, and has been widely studied. Embedding-based methods require training on complex queries and may not generalize well to out-of-distribution query structures. Recent work frames this task as an end-to-end optimization problem, and it only requires a pretrained link predictor. However, due to the exponentially large combinatorial search space, the optimal solution can only be approximated, limiting the final accuracy. In this work, we propose QTO (Query Computation Tree Optimization) that can efficiently find the exact optimal solution. QTO finds the optimal solution by a forward-backward propagation on the tree-like computation graph, i.e., query computation tree. In particular, QTO utilizes the independence encoded in the query computation tree to reduce the search space, where only local computations are involved during the optimization procedure. Experiments on 3 datasets show that QTO obtains state-of-the-art performance on complex query answering, outperforming previous best results by an average of 22%. Moreover, QTO can interpret the intermediate solutions for each of the one-hop atoms in the query with over 90% accuracy.

We propose Beam Tree Recursive Cell (BT-Cell) - a backpropagation-friendly framework to extend Recursive Neural Networks (RvNNs) with beam search for latent structure induction. We further extend this framework by proposing a relaxation of the hard top-$k$ operators in beam search for better propagation of gradient signals. We evaluate our proposed models in different out-of-distribution splits in both synthetic and realistic data. Our experiments show that BT-Cell achieves near-perfect performance on several challenging structure-sensitive synthetic tasks like ListOps and logical inference while maintaining comparable performance in realistic data against other RvNN-based models. Additionally, we identify a previously unknown failure case for neural models in generalization to unseen number of arguments in ListOps. The code is available at: https://github.com/JRC1995/BeamTreeRecursiveCells.

In Reinforcement Learning (RL), an agent acts in an unknown environment to maximize the expected cumulative discounted sum of an external reward signal, i.e., the expected return. In practice, in many tasks of interest, such as policy optimization, the agent usually spends its interaction budget by collecting episodes of *fixed length* within a simulator (i.e., Monte Carlo simulation). However, given the discounted nature of the RL objective, this data collection strategy might not be the best option. Indeed, the rewards taken in early simulation steps weigh exponentially more than future rewards. Taking a cue from this intuition, in this paper, we design an a-priori budget allocation strategy that leads to the collection of trajectories of different lengths, i.e., *truncated*. The proposed approach provably minimizes the width of the confidence intervals around the empirical estimates of the expected return of a policy. After discussing the theoretical properties of our method, we make use of our trajectory truncation mechanism to extend Policy Optimization via Importance Sampling (POIS, Metelli et al., 2018) algorithm. Finally, we conduct a numerical comparison between our algorithm and POIS: the results are consistent with our theory and show that an appropriate truncation of the trajectories can succeed in improving performance.

Automatic quantum architecture search (QAS) has been widely studied across disciplines with different implications. In this paper, beyond a particular domain, we formulate the QAS problem into two basic (and relatively even ideal) tasks: i) arbitrary quantum circuit (QC) regeneration given a target QC; ii) approximating an arbitrary unitary (oracle). The latter can be connected to the setting of various quantum machine learning tasks and other QAS applications. Based on these two tasks, we generate a public QAS benchmark including 900 random QCs and 400 random unitary matrices which is still missing in the literature. We evaluate six baseline algorithms including brute force search, simulated annealing, genetic algorithm, reinforcement learning, hybrid algorithm, and differentiable algorithm as part of our benchmark. One characteristic of our proposed evaluation protocol on the basic tasks is that it deprives the domain-specific designs and techniques as used in existing QAS literature, making a unified evaluation possible and focusing on the vanilla search methods themselves without coupling with domain prior. In fact, the unitary approximation task could be algorithmically more difficult than the specific problems as it needs to explore the whole matrix space to fit the unitary. While specific tasks often only need to fit a partial observation of the unitary as the objective for search. Data and code are available at https://github.com/Lucky-Lance/QAS-Bench.

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call **M**ulti-level **A**ctor-**C**ritic (MAC), is developed specifically for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it is therefore readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to SOTA actor-critic algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.

Given a reference set R of n points and a query set Q of m points in a metric space, this paper studies an important problem of finding k-nearest neighbors of every point q of Q in the set R in a near-linear time. In the paper at ICML 2006, Beygelzimer, Kakade, and Langford introduced a cover tree and attempted to prove that this tree can be built in O(n log n) time while the nearest neighbor search can be done O(n log m) time with a hidden dimensionality factor. In 2015, section 5.3 of Curtin's PhD pointed out that the proof of the latter claim can have a serious gap in time complexity estimation. A paper at TopoInVis 2022 reported explicit counterexamples for a key step in the proofs of both claims. The past obstacles will be overcome by a simpler compressed cover tree on the reference set R. The first new algorithm constructs a compressed cover tree in O(n log n) time. The second new algorithm finds all k-nearest neighbors of all points from Q using a compressed cover tree in time O(m(k+log n)log k) with a hidden dimensionality factor depending on point distributions of the sets R,Q but not on their sizes.

In recent years, online search has been playing an increasingly important role in imperfect information games (IIGs). Previous online search is known as common-knowledge subgame solving, which has to consider all the states in a common-knowledge closure. This is only computationally tolerable for medium size games, such as poker. To handle larger games, order-1 Knowledge-Limited Subgame Solving (1-KLSS) only considers the states in a knowledge-limited closure, which results in a much smaller subgame. However, 1-KLSS is unsafe. In this paper, we first extend 1-KLSS to Safe-1-KLSS and prove its safeness. To make Safe-1-KLSS applicable to even larger games, we propose Opponent-Limited Subgame Solving (OLSS) to limit how the opponent reaches a subgame and how it acts in the subgame. Limiting the opponent's strategy dramatically reduces the subgame size and improves the efficiency of subgame solving while still preserving some safety in the limit. Experiments in medium size poker show that Safe-1-KLSS and OLSS are orders of magnitude faster than previous common-knowledge subgame solving. Also, OLSS significantly improves the online performance in a two-player Mahjong game, whose game size prohibits the use of previous common-knowledge subgame-solving methods.

DARTS search space (DSS) has become a canonical benchmark for NAS whereas some emerging works pointed out the issue of narrow accuracy range and claimed it would hurt the method ranking. We observe some recent studies already suffer from this issue that overshadows the meaning of scores. In this work, we first propose and orchestrate a suite of improvements to frame a larger and harder DSS, termed LHD, while retaining high efficiency in search. We step forward to renovate a LHD-based new benchmark, taking care of both discernibility and accessibility. Specifically, we re-implement twelve baselines and evaluate them across twelve conditions by combining two underexpolored influential factors: transductive robustness and discretization policy, to reasonably construct a benchmark upon multi-condition evaluation. Considering that the tabular benchmarks are always insufficient to adequately evaluate the methods of neural architecture search (NAS), our work can serve as a crucial basis for the future progress of NAS.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.