Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as lakes. Traditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function (RBF) kernel cannot accommodate these complex constrained conditions. The In-BO uses the Sparse Intrinsic Gaussian Processes (SIn-GP) surrogate model to take into account the geometric structure of the manifold. SInGPs are constructed using the heat kernel of the manifold which is estimated as the transition density of the Brownian Motion on manifolds. The efficiency of In-BO is demonstrated through simulation studies on a U-shaped domain, a Bitten torus, and a real dataset from the Aral sea. Its performance is compared to that of traditional BO, which is defined in Euclidean space.

Ensemble methods can deliver surprising performance gains but also bring significantly higher computational costs, e.g., can be up to 2048X in large-scale ensemble tasks. However, we found that the majority of computations in ensemble methods are redundant. For instance, over 77% of samples in CIFAR-100 dataset can be correctly classified with only a single ResNet-18 model, which indicates that only around 23% of the samples need an ensemble of extra models. To this end, we propose an inference efficient ensemble learning method, to simultaneously optimize for effectiveness and efficiency in ensemble learning. More specifically, we regard ensemble of models as a sequential inference process and learn the optimal halting event for inference on a specific sample. At each timestep of the inference process, a common selector judges if the current ensemble has reached ensemble effectiveness and halt further inference, otherwise filters this challenging sample for the subsequent models to conduct more powerful ensemble. Both the base models and common selector are jointly optimized to dynamically adjust ensemble inference for different samples with various hardness, through the novel optimization goals including sequential ensemble boosting and computation saving. The experiments with different backbones on real-world datasets illustrate our method can bring up to 56\% inference cost reduction while maintaining comparable performance to full ensemble, achieving significantly better ensemble utility than other baselines. Code and supplemental materials are available at https://seqml.github.io/irene.

Optimization of atomic structures presents a challenging problem, due to their highly rough and non-convex energy landscape, with wide applications in the fields of drug design, materials discovery, and mechanics. Here, we present a graph reinforcement learning approach, StriderNET, that learns a policy to displace the atoms towards low energy configurations. We evaluate the performance of StriderNET on three complex atomic systems, namely, binary Lennard-Jones particles, calcium silicate hydrates gel, and disordered silicon. We show that StriderNET outperforms all classical optimization algorithms and enables the discovery of a lower energy minimum. In addition, StriderNET exhibits a higher rate of reaching minima with energies, as confirmed by the average over multiple realizations. Finally, we show that StriderNET exhibits inductivity to unseen system sizes that are an order of magnitude different from the training system.

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and then we propose an interacting particle scheme that approximates a Reweighted Interacting Langevin Diffusion system (RILD). The underlying system is designed by adding a multiplicative source term into the classical Langevin operator, leading to a higher convergence rate and a more concentrated invariant measure. We analyze the convergence rate of our algorithm and the improvement compared to existing results in the asymptotic situation. We also design various tests to verify our theoretical results, showing the advantages of accelerating convergence and breaking through barriers of suspicious local minimums, especially in high-dimensional non-convex settings. Our algorithms and analysis shed some light on combining gradient and genetic algorithms using Partial Differential Equations (PDEs) with provable guarantees.

Online resource allocation is a prominent paradigm for sequential decision making during a finite horizon subject to the resource constraints, increasingly attracting the wide attention of researchers and practitioners in theoretical computer science (Mehta et al., 2007; Devanur and Jain, 2012; Devanur et al., 2019), operations research (Agrawal et al., 2014; Li and Ye, 2021) and machine learning communities (Balseiro et al., 2020; Li et al., 2020). In these settings, the requests arrive online and we need to serve each request via one of the available channels, which consumes a certain amount of resources and generates a corresponding service charge. The objective of the decision maker is to maximize the cumulative revenue subject to the resource capacity constraints. Such problem frequently appears in many applications including online advertising (Mehta et al., 2007; Buchbinder et al., 2007), online combinatorial auctions (Chawla et al., 2010), online linear programming(Agrawal et al., 2014; Buchbinder and Naor, 2009), online routing(Buchbinder and Naor, 2006), online multi-leg flight seats and hotel rooms allocation (Talluri et al., 2004), etc. The aforementioned online resource allocation framework only considers the capacity (upper bound) constraints for resources.

The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML). These successes offer clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly affect humans. Unfortunately, the operation of the most successful ML models is incomprehensible for human decision makers. As a result, the use of ML models, especially in high-risk and safety-critical settings is not without concern. In recent years, there have been efforts on devising approaches for explaining ML models. Most of these efforts have focused on so-called model-agnostic approaches. However, all model-agnostic and related approaches offer no guarantees of rigor, hence being referred to as non-formal. For example, such non-formal explanations can be consistent with different predictions, which renders them useless in practice. This paper overviews the ongoing research efforts on computing rigorous model-based explanations of ML models; these being referred to as formal explanations. These efforts encompass a variety of topics, that include the actual definitions of explanations, the characterization of the complexity of computing explanations, the currently best logical encodings for reasoning about different ML models, and also how to make explanations interpretable for human decision makers, among others.

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient descent largely without adapting to the non-convex nature of the problem and can be sensitive to initial values, impeding further performance improvement. In this paper, we propose an efficient amortized optimization scheme for inverse problems with a deep generative prior. Specifically, the optimization task with high degrees of difficulty is decomposed into optimizing a sequence of much easier ones. We provide a theoretical guarantee of the proposed algorithm and empirically validate it on different inverse problems. As a result, our approach outperforms baseline methods qualitatively and quantitatively by a large margin.

Semidefinite programs (SDPs) are convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to make an efficient use of the current generation of quantum hardware. However, optimizing variational quantum algorithms is a challenge as it is an NP-hard problem that in general requires an exponential time to solve and can contain many far from optimal local minima. Here, we present a current term NISQ algorithm for solving SDPs. The classical optimization program of our NISQ solver is another SDP over a lower dimensional ansatz space. We harness the SDP based formulation of the Hamiltonian ground state problem to design a NISQ eigensolver. Unlike variational quantum eigensolvers, the classical optimization program of our eigensolver is convex, can be solved in polynomial time with the number of ansatz parameters and every local minimum is a global minimum. We find numeric evidence that NISQ SDP can improve the estimation of ground state energies in a scalable manner. Further, we efficiently solve constrained problems to calculate the excited states of Hamiltonians, find the lowest energy of symmetry constrained Hamiltonians and determine the optimal measurements for quantum state discrimination. We demonstrate the potential of our approach by finding the largest eigenvalue of up to $2^{1000}$ dimensional matrices and solving graph problems related to quantum contextuality. We also discuss NISQ algorithms for rank-constrained SDPs. Our work extends the application of NISQ computers onto one of the most successful algorithmic frameworks of the past few decades.

This paper presents a visual SLAM system that uses both points and lines for robust camera localization, and simultaneously performs a piece-wise planar reconstruction (PPR) of the environment to provide a structural map in real-time. One of the biggest challenges in parallel tracking and mapping with a monocular camera is to keep the scale consistent when reconstructing the geometric primitives. This further introduces difficulties in graph optimization of the bundle adjustment (BA) step. We solve these problems by proposing several run-time optimizations on the reconstructed lines and planes. Our system is able to run with depth and stereo sensors in addition to the monocular setting. Our proposed SLAM tightly incorporates the semantic and geometric features to boost both frontend pose tracking and backend map optimization. We evaluate our system exhaustively on various datasets, and show that we outperform state-of-the-art methods in terms of trajectory precision. The code of PLP-SLAM has been made available in open-source for the research community (https://github.com/PeterFWS/Structure-PLP-SLAM).

We study the problem of performance optimization of closed-loop control systems with unmodeled dynamics. Bayesian optimization (BO) has been demonstrated to be effective for improving closed-loop performance by automatically tuning controller gains or reference setpoints in a model-free manner. However, BO methods have rarely been tested on dynamical systems with unmodeled constraints and time-varying ambient conditions. In this paper, we propose a violation-aware contextual BO algorithm (VACBO) that optimizes closed-loop performance while simultaneously learning constraint-feasible solutions under time-varying ambient conditions. Unlike classical constrained BO methods which allow unlimited constraint violations, or 'safe' BO algorithms that are conservative and try to operate with near-zero violations, we allow budgeted constraint violations to improve constraint learning and accelerate optimization. We demonstrate the effectiveness of our proposed VACBO method for energy minimization of industrial vapor compression systems under time-varying ambient temperature and humidity.