Heuristic algorithms such as simulated annealing, Concorde, and METIS are effective and widely used approaches to find solutions to combinatorial optimization problems. However, they are limited by the high sample complexity required to reach a reasonable solution from a cold-start. In this paper, we introduce a novel framework to generate better initial solutions for heuristic algorithms using reinforcement learning (RL), named RLHO. We augment the ability of heuristic algorithms to greedily improve upon an existing initial solution generated by RL, and demonstrate novel results where RL is able to leverage the performance of heuristics as a learning signal to generate better initialization. We apply this framework to Proximal Policy Optimization (PPO) and Simulated Annealing (SA). We conduct a series of experiments on the well-known NP-complete bin packing problem, and show that the RLHO method outperforms our baselines. We show that on the bin packing problem, RL can learn to help heuristics perform even better, allowing us to combine the best parts of both approaches.

In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain of the problem. We extend the cooperative stochastic approximation algorithm from Lan and Zhou [2016] to solve the particular problem. We close the gaps in the previous analysis and provide a novel proof technique to show that our algorithm attains the optimal rate of convergence for both optimality gap and constraint violation when the functions are generally convex. We also compare our algorithm empirically to the state-of-the-art and show improved convergence in many situations.

Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimization algorithm that uses a combination of inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account by the approach. Compared to Bayesian optimization, the proposed algorithm is computationally lighter and, as we show in a set of benchmark global optimization and hyperparameter tuning problems, it has a very similar (and sometimes superior) performance. MATLAB and Python implementations of the proposed approach are available at http://cse.lab.imtlucca.it/~bemporad/idwgopt

Sustainable Supply Chain (SSC) management aims at integrating economic, environmental and social goals to assist in the long-term planning of a company and its supply chains. There is no consensus in the literature as to whether social and environmental responsibilities are profit-compatible. However, the conflicting nature of these goals is explicit when considering specific assessment measures and, in this scenario, multi-objective optimization is a way to represent problems that simultaneously optimize the goals. This paper proposes a Lagrangian matheuristic method, called $AugMathLagr$, to solve a hard and relevant multi-objective problem found in the literature. $AugMathLagr$ was extensively tested using artificial instances defined by a generator presented in this paper. The results show a competitive performance of $AugMathLagr$ when compared with an exact multi-objective method limited by time and a matheuristic recently proposed in the literature and adapted here to address the studied problem. In addition, computational results on a case study are presented and analyzed, and demonstrate the outstanding performance of $AugMathLagr$.

Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and dynamic programming.

Distributed optimization often consists of two updating phases: local optimization and inter-node communication. Conventional approaches require working nodes to communicate with the server every one or few iterations to guarantee convergence. In this paper, we establish a completely different conclusion that each node can perform an arbitrary number of local optimization steps before communication. Moreover, we show that the more local updating can reduce the overall communication, even for an infinity number of steps where each node is free to update its local model to near-optimality before exchanging information. The extra assumption we make is that the optimal sets of local loss functions have a non-empty intersection, which is inspired by the over-paramterization phenomenon in large-scale optimization and deep learning. Our theoretical findings are confirmed by both distributed convex optimization and deep learning experiments.

In this paper, we shall study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization perspective (previous work has only focused on variants of robust submodular maximization). We do this under a broad range of combinatorial constraints including cardinality, knapsack, matroid as well as graph based constraints such as cuts, paths, matchings and trees. Furthermore, we also study robust submodular minimization and maximization under multiple submodular upper and lower bound constraints. We show that all these problems are motivated by important machine learning applications including robust data subset selection, robust co-operative cuts and robust co-operative matchings. In each case, we provide scalable approximation algorithms and also study hardness bounds. Finally, we empirically demonstrate the utility of our algorithms on real world applications.

Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the clustering result. However, such a stepwise manner may make the constructed graph not fit the requirements for the subsequent decomposition, leading to compromised clustering accuracy. To this end, we propose a joint learning framework, which is able to learn the graph and the clustering result simultaneously, such that the resulting graph is tailored to the clustering task. The proposed model is formulated as a well-defined nonnegative and off-diagonal constrained optimization problem, which is further efficiently solved with convergence theoretically guaranteed. The advantage of the proposed model is demonstrated by comparing with 19 state-of-the-art clustering methods on 10 datasets with 4 clustering metrics.

A common dilemma encountered by many upon implementing an optimization method or experiment, whether it be a reinforcement learning algorithm, or A/B testing, is deciding on what metric to optimize for. Very often short-term metrics, which are easier to measure are chosen over long term metrics which have undesirable time considerations and often a more complex calculation. In this paper, we argue the importance of choosing a metrics that focuses on long term effects. With this comes the necessity in the ability to measure significant differences between groups relatively early. We present here an efficient methodology for early detection of lifetime differences between groups based on bootstrap hypothesis testing of the lifetime forecast of the response. We present an application of this method in the domain of online advertising and we argue that approach not only allows one to focus on the ultimate metric of importance but also provides a means of accelerating the testing period.

Observer effect in physics (/psychology) regards bias in measurement (/perception) due to the interference of instrument (/knowledge). Based on these concepts, a new meta-heuristic algorithm is proposed for controlling memory usage per localities without pursuing Tabu-like cut-off approaches. In this paper, first, variations of observer effect are explained in different branches of science from physics to psychology. Then, a metaheuristic algorithm is proposed based on observer effect concepts and the used metrics are explained. The derived optimizer performance has been compared between 1st, non-homogeneous-peaks-density functions, and 2nd, homogeneous-peaks-density functions to verify the algorithm outperformance in the 1st scheme. Finally, performance analysis of the novel algorithms is derived using two real-world engineering applications in Electroencephalogram feature learning and Distributed Generator parameter tuning, each of which having nonlinearity and complex multi-modal peaks distributions as its characteristics. Also, the effect of version improvement has been assessed. The performance analysis among other optimizers in the same context suggests that the proposed algorithm is useful both solely and in hybrid Gradient Descent settings where problem's search space is nonhomogeneous in terms of local peaks density.