Learning context-aware adaptive solvers to accelerate quadratic programming

Convex quadratic programming (QP) is an important sub-field of mathematical optimization. The alternating direction method of multipliers (ADMM) is a successful method to solve QP. Even though ADMM shows promising results in solving various types of QP, its convergence speed is known to be highly dependent on the step-size parameter $\rho$. Due to the absence of a general rule for setting $\rho$, it is often tuned manually or heuristically. In this paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to adaptively adjust $\rho$ to accelerate ADMM. CA-ADMM extracts the spatio-temporal context, which captures the dependency of the primal and dual variables of QP and their temporal evolution during the ADMM iterations. CA-ADMM chooses $\rho$ based on the extracted context. Through extensive numerical experiments, we validated that CA-ADMM effectively generalizes to unseen QP problems with different sizes and classes (i.e., having different QP parameter structures). Furthermore, we verified that CA-ADMM could dynamically adjust $\rho$ considering the stage of the optimization process to accelerate the convergence speed further.Comment: 9 pages, 4 figure

Learning scalable and transferable multi-robot/machine sequential assignment planning via graph embedding

Can the success of reinforcement learning methods for simple combinatorial optimization problems be extended to multi-robot sequential assignment planning? In addition to the challenge of achieving near-optimal performance in large problems, transferability to an unseen number of robots and tasks is another key challenge for real-world applications. In this paper, we suggest a method that achieves the first success in both challenges for robot/machine scheduling problems. Our method comprises of three components. First, we show a robot scheduling problem can be expressed as a random probabilistic graphical model (PGM). We develop a mean-field inference method for random PGM and use it for Q-function inference. Second, we show that transferability can be achieved by carefully designing two-step sequential encoding of problem state. Third, we resolve the computational scalability issue of fitted Q-iteration by suggesting a heuristic auction-based Q-iteration fitting method enabled by transferability we achieved. We apply our method to discrete-time, discrete space problems (Multi-Robot Reward Collection (MRRC)) and scalably achieve 97% optimality with transferability. This optimality is maintained under stochastic contexts. By extending our method to continuous time, continuous space formulation, we claim to be the first learning-based method with scalable performance among multi-machine scheduling problems; our method scalability achieves comparable performance to popular metaheuristics in Identical parallel machine scheduling (IPMS) problems

WATTNet: Learning to Trade FX via Hierarchical Spatio-Temporal Representation of Highly Multivariate Time Series

Finance is a particularly challenging application area for deep learning models due to low noise-to-signal ratio, non-stationarity, and partial observability. Non-deliverable-forwards (NDF), a derivatives contract used in foreign exchange (FX) trading, presents additional difficulty in the form of long-term planning required for an effective selection of start and end date of the contract. In this work, we focus on tackling the problem of NDF tenor selection by leveraging high-dimensional sequential data consisting of spot rates, technical indicators and expert tenor patterns. To this end, we construct a dataset from the Depository Trust & Clearing Corporation (DTCC) NDF data that includes a comprehensive list of NDF volumes and daily spot rates for 64 FX pairs. We introduce WaveATTentionNet (WATTNet), a novel temporal convolution (TCN) model for spatio-temporal modeling of highly multivariate time series, and validate it across NDF markets with varying degrees of dissimilarity between the training and test periods in terms of volatility and general market regimes. The proposed method achieves a significant positive return on investment (ROI) in all NDF markets under analysis, outperforming recurrent and classical baselines by a wide margin. Finally, we propose two orthogonal interpretability approaches to verify noise stability and detect the driving factors of the learned tenor selection strategy.Comment: Submitted to the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI 20

Genetic Algorithms with Neural Cost Predictor for Solving Hierarchical Vehicle Routing Problems

When vehicle routing decisions are intertwined with higher-level decisions, the resulting optimization problems pose significant challenges for computation. Examples are the multi-depot vehicle routing problem (MDVRP), where customers are assigned to depots before delivery, and the capacitated location routing problem (CLRP), where the locations of depots should be determined first. A simple and straightforward approach for such hierarchical problems would be to separate the higher-level decisions from the complicated vehicle routing decisions. For each higher-level decision candidate, we may evaluate the underlying vehicle routing problems to assess the candidate. As this approach requires solving vehicle routing problems multiple times, it has been regarded as impractical in most cases. We propose a novel deep-learning-based approach called Genetic Algorithm with Neural Cost Predictor (GANCP) to tackle the challenge and simplify algorithm developments. For each higher-level decision candidate, we predict the objective function values of the underlying vehicle routing problems using a pre-trained graph neural network without actually solving the routing problems. In particular, our proposed neural network learns the objective values of the HGS-CVRP open-source package that solves capacitated vehicle routing problems. Our numerical experiments show that this simplified approach is effective and efficient in generating high-quality solutions for both MDVRP and CLRP and has the potential to expedite algorithm developments for complicated hierarchical problems. We provide computational results evaluated in the standard benchmark instances used in the literature

A Neural Separation Algorithm for the Rounded Capacity Inequalities

The cutting plane method is a key technique for successful branch-and-cut and branch-price-and-cut algorithms that find the exact optimal solutions for various vehicle routing problems (VRPs). Among various cuts, the rounded capacity inequalities (RCIs) are the most fundamental. To generate RCIs, we need to solve the separation problem, whose exact solution takes a long time to obtain; therefore, heuristic methods are widely used. We design a learning-based separation heuristic algorithm with graph coarsening that learns the solutions of the exact separation problem with a graph neural network (GNN), which is trained with small instances of 50 to 100 customers. We embed our separation algorithm within the cutting plane method to find a lower bound for the capacitated VRP (CVRP) with up to 1,000 customers. We compare the performance of our approach with CVRPSEP, a popular separation software package for various cuts used in solving VRPs. Our computational results show that our approach finds better lower bounds than CVRPSEP for large-scale problems with 400 or more customers, while CVRPSEP shows strong competency for problems with less than 400 customers

Multi-Agent Actor-Critic with Hierarchical Graph Attention Network

Most previous studies on multi-agent reinforcement learning focus on deriving decentralized and cooperative policies to maximize a common reward and rarely consider the transferability of trained policies to new tasks. This prevents such policies from being applied to more complex multi-agent tasks. To resolve these limitations, we propose a model that conducts both representation learning for multiple agents using hierarchical graph attention network and policy learning using multi-agent actor-critic. The hierarchical graph attention network is specially designed to model the hierarchical relationships among multiple agents that either cooperate or compete with each other to derive more advanced strategic policies. Two attention networks, the inter-agent and inter-group attention layers, are used to effectively model individual and group level interactions, respectively. The two attention networks have been proven to facilitate the transfer of learned policies to new tasks with different agent compositions and allow one to interpret the learned strategies. Empirically, we demonstrate that the proposed model outperforms existing methods in several mixed cooperative and competitive tasks.Comment: Accepted as a conference paper at the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20), New York, US