Bayesian optimisation is a powerful method for optimising black-box functions, popular in settings where the true function is expensive to evaluate and no gradient information is available. Bayesian optimisation can improve responses to many optimisation problems within climate change for which simulator models are unavailable or expensive to sample from. While there have been several feasibility demonstrations of Bayesian optimisation in climate-related applications, there has been no unifying review of applications and benchmarks. We provide such a review here, to encourage the use of Bayesian optimisation in important and well-suited application domains. We identify four main application domains: material discovery, wind farm layout, optimal renewable control and environmental monitoring. For each domain we identify a public benchmark or data set that is easy to use and evaluate systems against, while being representative of real-world problems. Due to the lack of a suitable benchmark for environmental monitoring, we propose LAQN-BO, based on air pollution data. Our contributions are: a) identifying a representative range of benchmarks, providing example code where necessary; b) introducing a new benchmark, LAQN-BO; and c) promoting a wider use of climate change applications among Bayesian optimisation practitioners.

Collaborative Mobile Crowd Sensing (CMCS) enhances data quality and coverage by promoting teamwork in task sensing, with worker recruitment representing a complex multi-objective optimization problem. Existing strategies mainly focus on the characteristics of workers themselves, neglecting the asymmetric trust relationships between them, which affects the rationality of task utility evaluation. To address this, this paper first employs the Mini-Batch K-Means clustering algorithm and deploys edge servers to enable efficient distributed worker recruitment. Historical data and task requirements are utilized to obtain workers' ability types and distances. A trust-directed graph in the worker's social network is input into the Graph Convolutional Network (GCN) framework for training, capturing asymmetric trustworthiness between worker pairs. Privacy leakage is prevented in CMCS scenarios through high trust values between workers. Ultimately, an undirected recruitment graph is constructed using workers' abilities, trust values, and distance weights, transforming the worker recruitment problem into a Maximum Weight Average Subgraph Problem (MWASP). A Tabu Search Recruitment (TSR) algorithm is proposed to rationally recruit a balanced multi-objective optimal task utility worker set for each task. Extensive simulation experiments on four real-world datasets demonstrate the effectiveness of the proposed strategy, outperforming other strategies.

Learning a fair predictive model is crucial to mitigate biased decisions against minority groups in high-stakes applications. A common approach to learn such a model involves solving an optimization problem that maximizes the predictive power of the model under an appropriate group fairness constraint. However, in practice, sensitive attributes are often missing or noisy resulting in uncertainty. We demonstrate that solely enforcing fairness constraints on uncertain sensitive attributes can fall significantly short in achieving the level of fairness of models trained without uncertainty. To overcome this limitation, we propose a bootstrap-based algorithm that achieves the target level of fairness despite the uncertainty in sensitive attributes. The algorithm is guided by a Gaussian analysis for the independence notion of fairness where we propose a robust quadratically constrained quadratic problem to ensure a strict fairness guarantee with uncertain sensitive attributes. Our algorithm is applicable to both discrete and continuous sensitive attributes and is effective in real-world classification and regression tasks for various group fairness notions, e.g., independence and separation.

Optimization problems involving mixed variables, i.e., variables of numerical and categorical nature, can be challenging to solve, especially in the presence of complex constraints. Moreover, when the objective function is the result of a complicated simulation or experiment, it may be expensive to evaluate. This paper proposes a novel surrogate-based global optimization algorithm to solve linearly constrained mixed-variable problems up to medium-large size (around 100 variables after encoding and 20 constraints) based on constructing a piecewise affine surrogate of the objective function over feasible samples. We introduce two types of exploration functions to efficiently search the feasible domain via mixed-integer linear programming solvers. We also provide a preference-based version of the algorithm, which can be used when only pairwise comparisons between samples can be acquired while the underlying objective function to minimize remains unquantified. The two algorithms are tested on mixed-variable benchmark problems with and without constraints. The results show that, within a small number of acquisitions, the proposed algorithms can often achieve better or comparable results than other existing methods.

Robust Markov decision processes (RMDPs) provide a promising framework for computing reliable policies in the face of model errors. Many successful reinforcement learning algorithms build on variations of policy-gradient methods, but adapting these methods to RMDPs has been challenging. As a result, the applicability of RMDPs to large, practical domains remains limited. This paper proposes a new Double-Loop Robust Policy Gradient (DRPG), the first generic policy gradient method for RMDPs. In contrast with prior robust policy gradient algorithms, DRPG monotonically reduces approximation errors to guarantee convergence to a globally optimal policy in tabular RMDPs. We introduce a novel parametric transition kernel and solve the inner loop robust policy via a gradient-based method. Finally, our numerical results demonstrate the utility of our new algorithm and confirm its global convergence properties.

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 cannot 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. The code of our paper is at https://github.com/bys0318/QTO.

Privacy noise may negate the benefits of using adaptive optimizers in differentially private model training. Prior works typically address this issue by using auxiliary information (e.g., public data) to boost the effectiveness of adaptive optimization. In this work, we explore techniques to estimate and efficiently adapt to gradient geometry in private adaptive optimization without auxiliary data. Motivated by the observation that adaptive methods can tolerate stale preconditioners, we propose differentially private adaptive training with delayed preconditioners (DP^2), a simple method that constructs delayed but less noisy preconditioners to better realize the benefits of adaptivity. Theoretically, we provide convergence guarantees for our method for both convex and non-convex problems, and analyze trade-offs between delay and privacy noise reduction. Empirically, we explore DP^2 across several real-world datasets, demonstrating that it can improve convergence speed by as much as 4x relative to non-adaptive baselines and match the performance of state-of-the-art optimization methods that require auxiliary data.

Contrastive Learning has recently achieved state-of-the-art performance in a wide range of tasks. Many contrastive learning approaches use mined hard negatives to make batches more informative during training but these approaches are inefficient as they increase epoch length proportional to the number of mined negatives and require frequent updates of nearest neighbor indices or mining from recent batches. In this work, we provide an alternative to hard negative mining, Global Contrastive Batch Sampling (GCBS), an efficient approximation to the batch assignment problem that upper bounds the gap between the global and training losses, $\mathcal{L}^{Global} - \mathcal{L}^{Train}$, in contrastive learning settings. Through experimentation we find GCBS improves state-of-the-art performance in sentence embedding and code-search tasks. Additionally, GCBS is easy to implement as it requires only a few additional lines of code, does not maintain external data structures such as nearest neighbor indices, is more computationally efficient than the most minimal hard negative mining approaches, and makes no changes to the model being trained.

Evacuation planning is a crucial part of disaster management. However, joint optimization of its two essential components, routing and scheduling, with objectives such as minimizing average evacuation time or evacuation completion time, is a computationally hard problem. To approach it, we present MIP-LNS, a scalable optimization method that utilizes heuristic search with mathematical optimization and can optimize a variety of objective functions. We also present the method MIP-LNS-SIM, where we combine agent-based simulation with MIP-LNS to estimate delays due to congestion, as well as, find optimized plans considering such delays. We use Harris County in Houston, Texas, as our study area. We show that, within a given time limit, MIP-LNS finds better solutions than existing methods in terms of three different metrics. However, when congestion dependent delay is considered, MIP-LNS-SIM outperforms MIP-LNS in multiple performance metrics. In addition, MIP-LNS-SIM has a significantly lower percent error in estimated evacuation completion time compared to MIP-LNS.

To train image-caption retrieval (ICR) methods, contrastive loss functions are a common choice for optimization functions. Unfortunately, contrastive ICR methods are vulnerable to predictive feature suppression. Predictive features are features that correctly indicate the similarity between a query and a candidate item. However, in the presence of multiple predictive features during training, encoder models tend to suppress redundant predictive features, since these features are not needed to learn to discriminate between positive and negative pairs. While some predictive features are redundant during training, these features might be relevant during evaluation. We introduce an approach to reduce predictive feature suppression for resource-constrained ICR methods: latent target decoding (LTD). We add an additional decoder to the contrastive ICR framework, to reconstruct the input caption in a latent space of a general-purpose sentence encoder, which prevents the image and caption encoder from suppressing predictive features. We implement the LTD objective as an optimization constraint, to ensure that the reconstruction loss is below a bound value while primarily optimizing for the contrastive loss. Importantly, LTD does not depend on additional training data or expensive (hard) negative mining strategies. Our experiments show that, unlike reconstructing the input caption in the input space, LTD reduces predictive feature suppression, measured by obtaining higher recall@k, r-precision, and nDCG scores than a contrastive ICR baseline. Moreover, we show that LTD should be implemented as an optimization constraint instead of a dual optimization objective. Finally, we show that LTD can be used with different contrastive learning losses and a wide variety of resource-constrained ICR methods.