Search for: All records

We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical circuits cannot approximate even to TV distance $1-o(1)$. Prior work of Aaronson and Arkhipov (2011) showed such a separation for the case of exact sampling (i.e.~TV distance $$0$$), but separations for approximate sampling were only known for uniform algorithms. A key ingredient in our proof is a new hardness amplification lemma for the classical query complexity of the Yamakawa--Zhandry (2022) search problem. We show that the probability that any family of query algorithms collectively finds $$k$$ distinct solutions decays exponentially in $$k$$. 

This work quantifies the effect of misfit and threading dislocations on the surface energies of PbTe-PbSe interfaces, with the defect structures of the interfaces being obtained from atomistic and multiscale simulations of their manufacturing processes. Simulation results show that direct bonding produces semi-coherent interfaces with two-dimensional misfit dislocation networks, while heteroepitaxial processes produce complex three dimensional dislocation structures with both misfit and threading dislocations. Surface energies at these interfaces were determined by computing the interaction energies across these interfaces. Compared with coherent interfaces, directly bonded interfaces exhibit up to ~23% lower surface energy, while the surface energies of epitaxially grown interfaces can be nearly 50 % lower. The results demonstrate significant effects of dislocations on interfacial energy. 

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions - even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton 1993), where learners only have to succeed under samplable distributions. We study this distinction and show that samplable PAC substantially expands the power of efficient learners. We first construct a concept class that requires exponential sample complexity in standard PAC but is learnable with polynomial sample complexity in samplable PAC. We then lift this statistical separation to the computational setting and obtain a separation relative to a random oracle. Our proofs center around a new complexity primitive, explicit evasive sets, that we introduce and study. These are sets for which membership is easy to determine but are extremely hard to sample from. Our results extend to the online setting to similarly show that its landscape changes when the adversary is assumed to be efficient instead of computationally unbounded. 

Abstract We study certain polarized degenerations of Calabi–Yau manifolds near an intermediate complex structure limit, and improve the potential $C^0$C^{0}-convergence to a metric convergence result on the generic region for the corresponding collapsing Ricci-flat Kähler metrics. 

Many real-world situations allow for the acquisition of additional relevant information when making decisions with limited or uncertain data. However, traditional RL approaches either require all features to be acquired beforehand (e.g. in a MDP) or regard part of them as missing data that cannot be acquired (e.g. in a POMDP). In this work, we consider RL models that may actively acquire features from the environment to improve the decision quality and certainty, while automatically balancing the cost of feature acquisition process and the reward of task decision process. We propose the Active-Acquisition POMDP and identify two types of the acquisition process for different application domains. In order to assist the agent in the actively-acquired partially-observed environment and alleviate the exploration-exploitation dilemma, we develop a model-based approach, where a deep generative model is utilized to capture the dependencies of the features and impute the unobserved features. The imputations essentially represent the beliefs of the agent. Equipped with the dynamics model, we develop hierarchical RL algorithms to resolve both types of the AA-POMDPs. Empirical results demonstrate that our approach achieves considerably better performance than existing POMDP-RL solutions. 

Many real-world situations allow for the acquisition of additional relevant information when making decisions with limited or uncertain data. However, traditional RL approaches either require all features to be acquired beforehand (e.g. in a MDP) or regard part of them as missing data that cannot be acquired (e.g. in a POMDP). In this work, we consider RL models that may actively acquire features from the environment to improve the decision quality and certainty, while automatically balancing the cost of feature acquisition process and the reward of task decision process. We propose the Active-Acquisition POMDP and identify two types of the acquisition process for different application domains. In order to assist the agent in the actively-acquired partially-observed environment and alleviate the exploration-exploitation dilemma, we develop a model-based approach, where a deep generative model is utilized to capture the dependencies of the features and impute the unobserved features. The imputations essentially represent the beliefs of the agent. Equipped with the dynamics model, we develop hierarchical RL algorithms to resolve both types of the AA-POMDPs. Empirical results demonstrate that our approach achieves considerably better performance than existing POMDP-RL solutions 

The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and relevance. Towards addressing this, we prove a distributional-lifting theorem: This upgrades a learner that succeeds with respect to a limited distribution family \mathcal{D} to one that succeeds with respect to any distribution D^\star, with an efficiency overhead that scales with the complexity of expressing D^\star as a mixture of distributions in \mathcal{D}. Recent work of Blanc, Lange, Malik, and Tan considered the special case of lifting uniform-distribution learners and designed a lifter that uses a conditional sample oracle for D^\star, a strong form of access not afforded by the standard PAC model. Their approach, which draws on ideas from semi-supervised learning, first learns D^\star and then uses this information to lift. We show that their approach is information-theoretically intractable with access only to random examples, thereby giving formal justification for their use of the conditional sample oracle. We then take a different approach that sidesteps the need to learn D^\star, yielding a lifter that works in the standard PAC model and enjoys additional advantages: it works for all base distribution families, preserves the noise tolerance of learners, has better sample complexity, and is simpler. 

Recent studies and industry advancements indicate that modular vehicles (MVs) have the potential to enhance transportation systems through their ability to dock and split during a trip. Although various applications of MVs have been explored across different domains, their application in logistics remains underexplored. This study examines the use of MVs in cargo delivery to reduce total delivery costs. We model the delivery problem for MVs as a variant of the Vehicle Routing Problem, referred to as the Modular Vehicle Routing Problem (MVRP). In the MVRP, MVs can either serve customers independently or dock with other MVs to form a platoon, thereby reducing the average cost per unit. In this study, we mainly focus on two fundamental types of MVRPs, namely the capacitated MVRP (CMVRP) and the MVRP with time windows (MVRPTW). To address these problems, we first developed mixed-integer linear programming (MILP) models, which can be solved using commercial optimization solvers. Given the NP-hardness of this problem, we also designed a Tabu Search (TS) algorithm with a solution representation based on Gantt charts and a neighborhood structure tailored for the MVRP. Multi-start and shaking strategies were incorporated into the TS algorithm to escape local optima. Additionally, we explored other potential applications in logistics and discussed problem settings for three MVRP variants. Results from numerical experiments indicate that the proposed algorithm successfully identifies nearly all optimal solutions found by the MILP model in small-size benchmark instances, while also demonstrating good convergence speed in large-size benchmark instances. Comparative experiments show that the MVRP approach can reduce costs by approximately 5.6% compared to traditional delivery methods. Sensitivity analyses reveal that improving the cost-saving capability of MV platooning can enhance overall benefits. 

Abstract To ensure privacy protection and alleviate computational burden, we propose a fast subsmaling procedure for the Cox model with massive survival datasets from multi-centered, decentralized sources. The proposed estimator is computed based on optimal subsampling probabilities that we derived and enables transmission of subsample-based summary level statistics between different storage sites with only one round of communication. For inference, the asymptotic properties of the proposed estimator were rigorously established. An extensive simulation study demonstrated that the proposed approach is effective. The methodology was applied to analyze a large dataset from the U.S. airlines.