We consider the problem of recovering the causal structure underlying observations from different experimental conditions when the targets of the interventions in each experiment are unknown. We assume a linear structural causal model with additive Gaussian noise and consider interventions that perturb their targets while maintaining the causal relationships in the system. Different models may entail the same distributions, offering competing causal explanations for the given observations. We fully characterize this equivalence class and offer identifiability results, which we use to derive a greedy algorithm called GnIES to recover the equivalence class of the data-generating model without knowledge of the intervention targets. In addition, we develop a novel procedure to generate semi-synthetic data sets with known causal ground truth but distributions closely resembling those of a real data set of choice. We leverage this procedure and evaluate the performance of GnIES on synthetic, real, and semi-synthetic data sets. Despite the strong Gaussian distributional assumption, GnIES is robust to an array of model violations and competitive in recovering the causal structure in small- to large-sample settings. We provide, in the Python packages "gnies" and "sempler", implementations of GnIES and our semi-synthetic data generation procedure.

Heuristic search algorithms, e.g. A*, are the commonly used tools for pathfinding on grids, i.e. graphs of regular structure that are widely employed to represent environments in robotics, video games etc. Instance-independent heuristics for grid graphs, e.g. Manhattan distance, do not take the obstacles into account and, thus, the search led by such heuristics performs poorly in the obstacle-rich environments. To this end, we suggest learning the instance-dependent heuristic proxies that are supposed to notably increase the efficiency of the search. The first heuristic proxy we suggest to learn is the correction factor, i.e. the ratio between the instance independent cost-to-go estimate and the perfect one (computed offline at the training phase). Unlike learning the absolute values of the cost-to-go heuristic function, which was known before, when learning the correction factor the knowledge of the instance-independent heuristic is utilized. The second heuristic proxy is the path probability, which indicates how likely the grid cell is lying on the shortest path. This heuristic can be utilized in the Focal Search framework as the secondary heuristic, allowing us to preserve the guarantees on the bounded sub-optimality of the solution. We learn both suggested heuristics in a supervised fashion with the state-of-the-art neural networks containing attention blocks (transformers). We conduct a thorough empirical evaluation on a comprehensive dataset of planning tasks, showing that the suggested techniques i) reduce the computational effort of the A* up to a factor of $4$x while producing the solutions, which costs exceed the costs of the optimal solutions by less than $0.3$% on average; ii) outperform the competitors, which include the conventional techniques from the heuristic search, i.e. weighted A*, as well as the state-of-the-art learnable planners.

This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem, where one can not infer the loss incurred for selecting an action from observed feedback. We also introduce a new setup named Censored Semi Bandits, where the loss incurred for selecting an action can be observed under certain conditions. Finally, we study the channel selection problem in the communication networks, where the reward for an action is only observed when no other player selects that action to play in the round. These problems find applications in many fields like healthcare, crowd-sourcing, security, adaptive resource allocation, among many others. This thesis aims to address the above-described sequential decision problems by exploiting specific structures these problems exhibit. We develop provably optimal algorithms for each of these setups with weak feedback and validate their empirical performance on different problem instances derived from synthetic and real datasets.

This paper describes a Relevance-Zone pattern table (RZT) that can be used to replace a traditional transposition table. An RZT stores exact game values for patterns that are discovered during a Relevance-Zone-Based Search (RZS), which is the current state-of-the-art in solving L&D problems in Go. Positions that share the same pattern can reuse the same exact game value in the RZT. The pattern matching scheme for RZTs is implemented using a radix tree, taking into consideration patterns with different shapes. To improve the efficiency of table lookups, we designed a heuristic that prevents redundant lookups. The heuristic can safely skip previously queried patterns for a given position, reducing the overhead to 10% of the original cost. We also analyze the time complexity of the RZT both theoretically and empirically. Experiments show the overhead of traversing the radix tree in practice during lookup remain flat logarithmically in relation to the number of entries stored in the table. Experiments also show that the use of an RZT instead of a traditional transposition table significantly reduces the number of searched nodes on two data sets of 7x7 and 19x19 L&D Go problems.

This paper presents a methodology for integrating machine learning techniques into metaheuristics for solving combinatorial optimization problems. Namely, we propose a general machine learning framework for neighbor generation in metaheuristic search. We first define an efficient neighborhood structure constructed by applying a transformation to a selected subset of variables from the current solution. Then, the key of the proposed methodology is to generate promising neighbors by selecting a proper subset of variables that contains a descent of the objective in the solution space. To learn a good variable selection strategy, we formulate the problem as a classification task that exploits structural information from the characteristics of the problem and from high-quality solutions. We validate our methodology on two metaheuristic applications: a Tabu Search scheme for solving a Wireless Network Optimization problem and a Large Neighborhood Search heuristic for solving Mixed-Integer Programs. The experimental results show that our approach is able to achieve a satisfactory trade-off between the exploration of a larger solution space and the exploitation of high-quality solution regions on both applications.

This paper introduces a novel method of adding intrinsic bonuses to task-oriented reward function in order to efficiently facilitate reinforcement learning search. While various bonuses have been designed to date, they are analogous to the depth-first and breadth-first search algorithms in graph theory. This paper, therefore, first designs two bonuses for each of them. Then, a heuristic gain scheduling is applied to the designed bonuses, inspired by the iterative deepening search, which is known to inherit the advantages of the two search algorithms. The proposed method is expected to allow agent to efficiently reach the best solution in deeper states by gradually exploring unknown states. In three locomotion tasks with dense rewards and three simple tasks with sparse rewards, it is shown that the two types of bonuses contribute to the performance improvement of the different tasks complementarily. In addition, by combining them with the proposed gain scheduling, all tasks can be accomplished with high performance.

Algorithms that involve both forecasting and optimization are at the core of solutions to many difficult real-world problems, such as in supply chains (inventory optimization), traffic, and in the transition towards carbon-free energy generation in battery/load/production scheduling in sustainable energy systems. Typically, in these scenarios we want to solve an optimization problem that depends on unknown future values, which therefore need to be forecast. As both forecasting and optimization are difficult problems in their own right, relatively few research has been done in this area. This paper presents the findings of the ``IEEE-CIS Technical Challenge on Predict+Optimize for Renewable Energy Scheduling," held in 2021. We present a comparison and evaluation of the seven highest-ranked solutions in the competition, to provide researchers with a benchmark problem and to establish the state of the art for this benchmark, with the aim to foster and facilitate research in this area. The competition used data from the Monash Microgrid, as well as weather data and energy market data. It then focused on two main challenges: forecasting renewable energy production and demand, and obtaining an optimal schedule for the activities (lectures) and on-site batteries that lead to the lowest cost of energy. The most accurate forecasts were obtained by gradient-boosted tree and random forest models, and optimization was mostly performed using mixed integer linear and quadratic programming. The winning method predicted different scenarios and optimized over all scenarios jointly using a sample average approximation method.

Metaheuristics are popularly used in various fields, and they have attracted much attention in the scientific and industrial communities. In recent years, the number of new metaheuristic names has been continuously growing. Generally, the inventors attribute the novelties of these new algorithms to inspirations from either biology, human behaviors, physics, or other phenomena. In addition, these new algorithms, compared against basic versions of other metaheuristics using classical benchmark problems without shift/rotation, show competitive performances. In this study, we exhaustively tabulate more than 500 metaheuristics. To comparatively evaluate the performance of the recent competitive variants and newly proposed metaheuristics, 11 newly proposed metaheuristics and 4 variants of established metaheuristics are comprehensively compared on the CEC2017 benchmark suite. In addition, whether these algorithms have a search bias to the center of the search space is investigated. The results show that the performance of the newly proposed EBCM (effective butterfly optimizer with covariance matrix adaptation) algorithm performs comparably to the 4 well performing variants of the established metaheuristics and possesses similar properties and behaviors, such as convergence, diversity, exploration and exploitation trade-offs, in many aspects. The performance of all 15 of the algorithms is likely to deteriorate due to certain transformations, while the 4 state-of-the-art metaheuristics are less affected by transformations such as the shifting of the global optimal point away from the center of the search space. It should be noted that, except EBCM, the other 10 new algorithms proposed mostly during 2019-2020 are inferior to the well performing 2017 variants of differential evolution and evolution strategy in terms of convergence speed and global search ability on CEC 2017 functions.

In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some variables to be unobserved in the available data. We devote special attention to two fundamental combinatorial aspects of causal structure learning. First, we discuss the structure of the search space over causal graphs. Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can be refined by adding interventional data.

In a Go game, AlphaGo Zero uses MC Tree Search to build a local policy to sample the next move. MCTS searches for possible moves and records the results in a search tree. As more searches are performed, the tree grows larger as well as its information. To make a move in Alpha-Go Zero, 1,600 searches will be computed. Then a local policy is constructed.