The Multi-Commodity Pickup and Delivery Vehicle Routing Problem aims to optimize the pickup and delivery of multiple unique commodities using a fleet of several agents with limited payload capacities. This paper addresses the challenge of quickly recomputing the solution to this NP-hard problem when there are unexpected perturbations to the nominal task definitions, likely to occur under real-world operating conditions. The proposed method first decomposes the nominal problem by constructing a search tree using Monte Carlo Tree Search for task assignment, and uses a rapid heuristic for routing each agent. When changes to the problem are revealed, the nominal search tree is rapidly updated with new costs under the updated problem parameters, generating solutions quicker and with a reduced optimality gap, as compared to recomputing the solution as an entirely new problem. Computational experiments are conducted by varying the locations of the nominal problem and the payload capacity of an agent to demonstrate the effectiveness of utilizing the nominal search tree to handle perturbations for real-time implementation.

Strong foundations in basic AI techniques are key to understanding more advanced concepts. We believe that introducing AI techniques, such as search methods, early in higher education helps create a deeper understanding of the concepts seen later in more advanced AI and algorithms courses. We present a project-based and competition-based bachelor course that gives second-year students an introduction to search methods applied to board games. In groups of two, students have to use network programming and AI methods to build an AI agent to compete in a board game tournament-othello was this year's game. Students are evaluated based on the quality of their projects and on their performance during the final tournament. We believe that the introduction of gamification, in the form of competition-based learning, allows for a better learning experience for the students.

Neural Architecture Search (NAS) has become a popular method for discovering effective model architectures, especially for target hardware. As such, NAS methods that find optimal architectures under constraints are essential. In our paper, we propose LayerNAS to address the challenge of multi-objective NAS by transforming it into a combinatorial optimization problem, which effectively constrains the search complexity to be polynomial. For a model architecture with $L$ layers, we perform layerwise-search for each layer, selecting from a set of search options $\mathbb{S}$. LayerNAS groups model candidates based on one objective, such as model size or latency, and searches for the optimal model based on another objective, thereby splitting the cost and reward elements of the search. This approach limits the search complexity to $ O(H \cdot |\mathbb{S}| \cdot L) $, where $H$ is a constant set in LayerNAS. Our experiments show that LayerNAS is able to consistently discover superior models across a variety of search spaces in comparison to strong baselines, including search spaces derived from NATS-Bench, MobileNetV2 and MobileNetV3.

In this work, we propose the Informed Batch Belief Trees (IBBT) algorithm for motion planning under motion and sensing uncertainties. The original stochastic motion planning problem is divided into a deterministic motion planning problem and a graph search problem. We solve the deterministic planning problem using sampling-based methods such as PRM or RRG to construct a graph of nominal trajectories. Then, an informed cost-to-go heuristic for the original problem is computed based on the nominal trajectory graph. Finally, we grow a belief tree by searching over the graph using the proposed heuristic. IBBT interleaves between batch state sampling, nominal trajectory graph construction, heuristic computing, and search over the graph to find belief space motion plans. IBBT is an anytime, incremental algorithm. With an increasing number of batches of samples added to the graph, the algorithm finds motion plans that converge to the optimal one. IBBT is efficient by reusing results between sequential iterations. The belief tree searching is an ordered search guided by an informed heuristic. We test IBBT in different planning environments. Our numerical investigation confirms that IBBT finds non-trivial motion plans and is faster compared with previous similar methods.

Classification trees continue to be widely adopted in machine learning applications due to their inherently interpretable nature and scalability. We propose a rolling subtree lookahead algorithm that combines the relative scalability of the myopic approaches with the foresight of the optimal approaches in constructing trees. The limited foresight embedded in our algorithm mitigates the learning pathology observed in optimal approaches. At the heart of our algorithm lies a novel two-depth optimal binary classification tree formulation flexible to handle any loss function. We show that the feasible region of this formulation is an integral polyhedron, yielding the LP relaxation solution optimal. Through extensive computational analyses, we demonstrate that our approach outperforms optimal and myopic approaches in 808 out of 1330 problem instances, improving the out-of-sample accuracy by up to 23.6% and 14.4%, respectively.

Minimax optimization plays an important role in many machine learning tasks such as generative adversarial networks (GANs) and adversarial training. Although recently a wide variety of optimization methods have been proposed to solve the minimax problems, most of them ignore the distributed setting where the data is distributed on multiple workers. Meanwhile, the existing decentralized minimax optimization methods rely on the strictly assumptions such as (strongly) concavity and variational inequality conditions. In the paper, thus, we propose an efficient decentralized momentum-based gradient descent ascent (DM-GDA) method for the distributed nonconvex-PL minimax optimization, which is nonconvex in primal variable and is nonconcave in dual variable and satisfies the Polyak-Lojasiewicz (PL) condition. In particular, our DM-GDA method simultaneously uses the momentum-based techniques to update variables and estimate the stochastic gradients. Moreover, we provide a solid convergence analysis for our DM-GDA method, and prove that it obtains a near-optimal gradient complexity of $O(\epsilon^{-3})$ for finding an $\epsilon$-stationary solution of the nonconvex-PL stochastic minimax problems, which reaches the lower bound of nonconvex stochastic optimization. To the best of our knowledge, we first study the decentralized algorithm for Nonconvex-PL stochastic minimax optimization over a network.

In this work, we develop the Batch Belief Trees (BBT) algorithm for motion planning under motion and sensing uncertainties. The algorithm interleaves between batch sampling, building a graph of nominal trajectories in the state space, and searching over the graph to find belief space motion plans. By searching over the graph, BBT finds sophisticated plans that will visit (and revisit) information-rich regions to reduce uncertainty. One of the key benefits of this algorithm is the modified interplay between exploration and exploitation. Instead of an exhaustive search (exploitation) after one exploration step, the proposed algorithm uses batch samples to explore the state space and, in addition, does not require exhaustive search before the next iteration of batch sampling, which adds flexibility.The algorithm finds motion plans that converge to the optimal one as more samples are added to the graph. We test BBT in different planning environments. Our numerical investigation confirms that BBT finds non-trivial motion plans and is faster compared with previous similar methods.

To meet the growing need for computational power for DNNs, multiple specialized hardware architectures have been proposed. Each DNN layer should be mapped onto the hardware with the most efficient schedule, however, SotA schedulers struggle to consistently provide optimum schedules in a reasonable time across all DNN-HW combinations. This paper proposes SALSA, a fast dual-engine scheduler to generate optimal execution schedules for both even and uneven mapping. We introduce a new strategy, combining exhaustive search with simulated annealing to address the dynamic nature of the loop ordering design space size across layers. SALSA is extensively benchmarked against two SotA schedulers, LOMA and Timeloop on 5 different DNNs, on average SALSA finds schedules with 11.9% and 7.6% lower energy while speeding up the search by 1.7x and 24x compared to LOMA and Timeloop, respectively.

Rewrite systems [6, 10, 12] have been widely employing equality saturation [9], which is an optimisation methodology that uses a saturated e-graph to represent all possible sequences of rewrite simultaneously, and then extracts the optimal one. As such, optimal results can be achieved by avoiding the phase-ordering problem. However, we observe that when the e-graph is not saturated, it cannot represent all possible rewrite opportunities and therefore the phase-ordering problem is re-introduced during the construction phase of the e-graph. To address this problem, we propose MCTS-GEB, a domain-general rewrite system that applies reinforcement learning (RL) to e-graph construction. At its core, MCTS-GEB uses a Monte Carlo Tree Search (MCTS) [3] to efficiently plan for the optimal e-graph construction, and therefore it can effectively eliminate the phase-ordering problem at the construction phase and achieve better performance within a reasonable time. Evaluation in two different domains shows MCTS-GEB can outperform the state-of-the-art rewrite systems by up to 49x, while the optimisation can generally take less than an hour, indicating MCTS-GEB is a promising building block for the future generation of rewrite systems.

Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep Reinforcement Learning (DRL) has been increasingly employed to solve TSP due to its high inference efficiency. Nevertheless, most of existing end-to-end DRL algorithms only perform well on small TSP instances and can hardly generalize to large scale because of the drastically soaring memory consumption and computation time along with the enlarging problem scale. In this paper, we propose a novel end-to-end DRL approach, referred to as Pointerformer, based on multi-pointer Transformer. Particularly, Pointerformer adopts both reversible residual network in the encoder and multi-pointer network in the decoder to effectively contain memory consumption of the encoder-decoder architecture. To further improve the performance of TSP solutions, Pointerformer employs both a feature augmentation method to explore the symmetries of TSP at both training and inference stages as well as an enhanced context embedding approach to include more comprehensive context information in the query. Extensive experiments on a randomly generated benchmark and a public benchmark have shown that, while achieving comparative results on most small-scale TSP instances as SOTA DRL approaches do, Pointerformer can also well generalize to large-scale TSPs.