Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade. However, most existing works focus on variants of gradient descent-ascent (GDA) algorithms, which are only applicable to smooth nonconvex-concave settings. To address this limitation, we propose a novel algorithm named smoothed proximal linear descent-ascent (smoothed PLDA), which can effectively handle a broad range of structured nonsmooth nonconvex-nonconcave minimax problems. Specifically, we consider the setting where the primal function has a nonsmooth composite structure and the dual function possesses the Kurdyka-Lojasiewicz (KL) property with exponent $\theta \in [0,1)$. We introduce a novel convergence analysis framework for smoothed PLDA, the key components of which are our newly developed nonsmooth primal error bound and dual error bound. Using this framework, we show that smoothed PLDA can find both $\epsilon$-game-stationary points and $\epsilon$-optimization-stationary points of the problems of interest in $\mathcal{O}(\epsilon^{-2\max\{2\theta,1\}})$ iterations. Furthermore, when $\theta \in [0,\frac{1}{2}]$, smoothed PLDA achieves the optimal iteration complexity of $\mathcal{O}(\epsilon^{-2})$. To further demonstrate the effectiveness and wide applicability of our analysis framework, we show that certain max-structured problem possesses the KL property with exponent $\theta=0$ under mild assumptions. As a by-product, we establish algorithm-independent quantitative relationships among various stationarity concepts, which may be of independent interest.

Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The MinDS problem is a classic $\mathcal{NP}$-hard problem and has been extensively studied because of its many disparate applications in network analysis. To solve this problem efficiently, many heuristic approaches have been proposed to obtain a good solution within an acceptable time limit. However, existing MinDS heuristic algorithms are always limited by various tie-breaking cases when selecting vertices, which slows down the effectiveness of the algorithms. In this paper, we design an efficient local search algorithm for the MinDS problem, named DmDS -- a dual-mode local search framework that probabilistically chooses between two distinct vertex-swapping schemes. We further address limitations of other algorithms by introducing vertex selection criterion based on the frequency of vertices added to solutions to address tie-breaking cases, and a new strategy to improve the quality of the initial solution via a greedy-based strategy integrated with perturbation. We evaluate DmDS against the state-of-the-art algorithms on seven datasets, consisting of 346 instances (or families) with up to tens of millions of vertices. Experimental results show that DmDS obtains the best performance in accuracy for almost all instances and finds much better solutions than state-of-the-art MinDS algorithms on a broad range of large real-world graphs.

Multi-Task Learning (MTL) aims to learn multiple tasks simultaneously while exploiting their mutual relationships. By using shared resources to simultaneously calculate multiple outputs, this learning paradigm has the potential to have lower memory requirements and inference times compared to the traditional approach of using separate methods for each task. Previous work in MTL has mainly focused on fully-supervised methods, as task relationships can not only be leveraged to lower the level of data-dependency of those methods but they can also improve performance. However, MTL introduces a set of challenges due to a complex optimisation scheme and a higher labeling requirement. This review focuses on how MTL could be utilised under different partial supervision settings to address these challenges. First, this review analyses how MTL traditionally uses different parameter sharing techniques to transfer knowledge in between tasks. Second, it presents the different challenges arising from such a multi-objective optimisation scheme. Third, it introduces how task groupings can be achieved by analysing task relationships. Fourth, it focuses on how partially supervised methods applied to MTL can tackle the aforementioned challenges. Lastly, this review presents the available datasets, tools and benchmarking results of such methods.

The rapid design of advanced materials is a topic of great scientific interest. The conventional, ``forward'' paradigm of materials design involves evaluating multiple candidates to determine the best candidate that matches the target properties. However, recent advances in the field of deep learning have given rise to the possibility of an ``inverse'' design paradigm for advanced materials, wherein a model provided with the target properties is able to find the best candidate. Being a relatively new concept, there remains a need to systematically evaluate how these two paradigms perform in practical applications. Therefore, the objective of this study is to directly, quantitatively compare the forward and inverse design modeling paradigms. We do so by considering two case studies of refractory high-entropy alloy design with different objectives and constraints and comparing the inverse design method to other forward schemes like localized forward search, high throughput screening, and multi objective optimization.

In this work we study a well-known and challenging problem of Multi-agent Pathfinding, when a set of agents is confined to a graph, each agent is assigned a unique start and goal vertices and the task is to find a set of collision-free paths (one for each agent) such that each agent reaches its respective goal. We investigate how to utilize Monte-Carlo Tree Search (MCTS) to solve the problem. Although MCTS was shown to demonstrate superior performance in a wide range of problems like playing antagonistic games (e.g. Go, Chess etc.), discovering faster matrix multiplication algorithms etc., its application to the problem at hand was not well studied before. To this end we introduce an original variant of MCTS, tailored to multi-agent pathfinding. The crux of our approach is how the reward, that guides MCTS, is computed. Specifically, we use individual paths to assist the agents with the the goal-reaching behavior, while leaving them freedom to get off the track if it is needed to avoid collisions. We also use a dedicated decomposition technique to reduce the branching factor of the tree search procedure. Empirically we show that the suggested method outperforms the baseline planning algorithm that invokes heuristic search, e.g.

Most of the existing methods are ad hoc, and do not have explicit Random forest is effective for prediction tasks control over the size and accuracy of a DT. For e.g., there are but the randomness of tree generation hinders interpretability greedy splitting-based (Quinlan, 1986; 2014; Breiman et al., in feature importance analysis. To 1984), Bayesian-based (Denison et al., 1998; Chipman et al., address this, we proposed DT-Sampler, a SATbased 1998; 2002; 2010; Letham et al., 2015), branch-and-bound method for measuring feature importance methods (Angelino et al., 2017) for DT construction.

Recent work on designing an appropriate distribution of environments has shown promise for training effective generally capable agents. Its success is partly because of a form of adaptive curriculum learning that generates environment instances (or levels) at the frontier of the agent's capabilities. However, such an environment design framework often struggles to find effective levels in challenging design spaces and requires costly interactions with the environment. In this paper, we aim to introduce diversity in the Unsupervised Environment Design (UED) framework. Specifically, we propose a task-agnostic method to identify observed/hidden states that are representative of a given level. The outcome of this method is then utilized to characterize the diversity between two levels, which as we show can be crucial to effective performance. In addition, to improve sampling efficiency, we incorporate the self-play technique that allows the environment generator to automatically generate environments that are of great benefit to the training agent. Quantitatively, our approach, Diversity-induced Environment Design via Self-Play (MBeDED), shows compelling performance over existing methods.

Symbolic task planning for robots is computationally challenging due to the combinatorial complexity of the possible action space. This fact is amplified if there are several sub-goals to be achieved due to the increased length of the action sequences. In this work, we propose a multi-goal symbolic task planner for deterministic decision processes based on Monte Carlo Tree Search. We augment the algorithm by prioritized node expansion which prioritizes nodes that already have fulfilled some sub-goals. Due to its linear complexity in the number of sub-goals, our algorithm is able to identify symbolic action sequences of 145 elements to reach the desired goal state with up to 48 sub-goals while the search tree is limited to under 6500 nodes. We use action reduction based on a kinematic reachability criterion to further ease computational complexity. We combine our algorithm with object localization and motion planning and apply it to a real-robot demonstration with two manipulators in an industrial bearing inspection setting.

Tree data are ubiquitous, especially in biology and computer science, but also non-Euclidean [9], which prevents them from being analysed by classical statistical methods adapted to multidimensional data. Therefore, they require the development of specific tools that take into account their structured nature. Among such techniques, frequent pattern mining [1] consists in identifying patterns, i.e. substructures, that appear often in the data. The more elaborate the patterns searched, the more difficult the problem is: the issue is to preserve a reasonable algorithmic complexity that allows the search of a given family of patterns in a reasonable time. Different types of patterns have been considered in the literature to analyse tree data (see the survey [16] and the references therein) with a strong interest in a specific family of patterns called subtrees [3, 23]. In these two papers, only subtrees that appear more often than a given threshold are considered. Reverse search [5] is a generic approach for enumerating frequent patterns in a dataset that consists in (i) building an enumeration tree of substructures, and then (ii) pruning it to keep only frequent patterns.

Autonomous robots have real-world applications in diverse fields, such as mobile manipulation and environmental exploration, and many such tasks benefit from a hands-off approach in terms of human user involvement over a long task horizon. However, the level of autonomy achievable by a deployment is limited in part by the problem definition or task specification required by the system. Task specifications often require technical, low-level information that is unintuitive to describe and may result in generic solutions, burdening the user technically both before and after task completion. In this thesis, we aim to advance task specification abstraction toward the goal of increasing robot autonomy in real-world scenarios. We do so by tackling problems that address several different angles of this goal. First, we develop a way for the automatic discovery of optimal transition points between subtasks in the context of constrained mobile manipulation, removing the need for the human to hand-specify these in the task specification. We further propose a way to automatically describe constraints on robot motion by using demonstrated data as opposed to manually-defined constraints. Then, within the context of environmental exploration, we propose a flexible task specification framework, requiring just a set of quantiles of interest from the user that allows the robot to directly suggest locations in the environment for the user to study. We next systematically study the effect of including a robot team in the task specification and show that multirobot teams have the ability to improve performance under certain specification conditions, including enabling inter-robot communication. Finally, we propose methods for a communication protocol that autonomously selects useful but limited information to share with the other robots.