We consider the problem of optimizing expensive black-box functions over high-dimensional combinatorial spaces which arises in many science, engineering, and ML applications. We use Bayesian Optimization (BO) and propose a novel surrogate modeling approach for efficiently handling a large number of binary and categorical parameters. The key idea is to select a number of discrete structures from the input space (the dictionary) and use them to define an ordinal embedding for high-dimensional combinatorial structures. This allows us to use existing Gaussian process models for continuous spaces. We develop a principled approach based on binary wavelets to construct dictionaries for binary spaces, and propose a randomized construction method that generalizes to categorical spaces. We provide theoretical justification to support the effectiveness of the dictionary-based embeddings. Our experiments on diverse real-world benchmarks demonstrate the effectiveness of our proposed surrogate modeling approach over state-of-the-art BO methods.

Concept learning deals with learning description logic concepts from a background knowledge and input examples. The goal is to learn a concept that covers all positive examples, while not covering any negative examples. This non-trivial task is often formulated as a search problem within an infinite quasi-ordered concept space. Although state-of-the-art models have been successfully applied to tackle this problem, their large-scale applications have been severely hindered due to their excessive exploration incurring impractical runtimes. Here, we propose a remedy for this limitation. We reformulate the learning problem as a multi-label classification problem and propose a neural embedding model (NERO) that learns permutation-invariant embeddings for sets of examples tailored towards predicting $F_1$ scores of pre-selected description logic concepts. By ranking such concepts in descending order of predicted scores, a possible goal concept can be detected within few retrieval operations, i.e., no excessive exploration. Importantly, top-ranked concepts can be used to start the search procedure of state-of-the-art symbolic models in multiple advantageous regions of a concept space, rather than starting it in the most general concept $\top$. Our experiments on 5 benchmark datasets with 770 learning problems firmly suggest that NERO significantly (p-value <1%) outperforms the state-of-the-art models in terms of $F_1$ score, the number of explored concepts, and the total runtime. We provide an open-source implementation of our approach.

In the wake of a cybersecurity incident, it is crucial to promptly discover how the threat actors breached security in order to assess the impact of the incident and to develop and deploy countermeasures that can protect against further attacks. To this end, defenders can launch a cyber-forensic investigation, which discovers the techniques that the threat actors used in the incident. A fundamental challenge in such an investigation is prioritizing the investigation of particular techniques since the investigation of each technique requires time and effort, but forensic analysts cannot know which ones were actually used before investigating them. To ensure prompt discovery, it is imperative to provide decision support that can help forensic analysts with this prioritization. A recent study demonstrated that data-driven decision support, based on a dataset of prior incidents, can provide state-of-the-art prioritization. However, this data-driven approach, called DISCLOSE, is based on a heuristic that utilizes only a subset of the available information and does not approximate optimal decisions. To improve upon this heuristic, we introduce a principled approach for data-driven decision support for cyber-forensic investigations. We formulate the decision-support problem using a Markov decision process, whose states represent the states of a forensic investigation. To solve the decision problem, we propose a Monte Carlo tree search based method, which relies on a k-NN regression over prior incidents to estimate state-transition probabilities. We evaluate our proposed approach on multiple versions of the MITRE ATT&CK dataset, which is a knowledge base of adversarial techniques and tactics based on real-world cyber incidents, and demonstrate that our approach outperforms DISCLOSE in terms of techniques discovered per effort spent.

Competitive influence maximization has been studied for several years, and various frameworks have been proposed to model different aspects of information diffusion under the competitive environment. This work presents a new gameboard for two competing parties with some new features representing loyalty in social networks and reflecting the attitude of not completely being loyal to a party when the opponent offers better suggestions. This behavior can be observed in most political occasions where each party tries to attract people by making better suggestions than the opponent and even seeks to impress the fans of the opposition party to change their minds. In order to identify the best move in each step of the game framework, an improved Monte Carlo tree search is developed, which uses some predefined heuristics to apply them on the simulation step of the algorithm and takes advantage of them to search among child nodes of the current state and pick the best one using an epsilon-greedy way instead of choosing them at random. Experimental results on synthetic and real datasets indicate the outperforming of the proposed strategy against some well-known and benchmark strategies like general MCTS, minimax algorithm with alpha-beta pruning, random nodes, nodes with maximum threshold and nodes with minimum threshold.

We study search problems that can be solved by performing Gradient Descent on a bounded convex polytopal domain and show that this class is equal to the intersection of two well-known classes: PPAD and PLS. As our main underlying technical contribution, we show that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain $[0,1]^2$ is PPAD $\cap$ PLS-complete. This is the first non-artificial problem to be shown complete for this class. Our results also imply that the class CLS (Continuous Local Search) - which was defined by Daskalakis and Papadimitriou as a more "natural" counterpart to PPAD $\cap$ PLS and contains many interesting problems - is itself equal to PPAD $\cap$ PLS.

With software systems becoming increasingly pervasive and autonomous, our ability to test for their quality is severely challenged. Many systems are called to operate in uncertain and highly-changing environment, not rarely required to make intelligent decisions by themselves. This easily results in an intractable state space to explore at testing time. The state-of-the-art techniques try to keep the pace, e.g., by augmenting the tester's intuition with some form of (explicit or implicit) learning from observations to search this space efficiently. For instance, they exploit historical data to drive the search (e.g., ML-driven testing) or the tests execution data itself (e.g., adaptive or search-based testing). Despite the indubitable advances, the need for smartening the search in such a huge space keeps to be pressing. We introduce Reasoning-Based Software Testing (RBST), a new way of thinking at the testing problem as a causal reasoning task. Compared to mere intuition-based or state-of-the-art learning-based strategies, we claim that causal reasoning more naturally emulates the process that a human would do to ''smartly" search the space. RBST aims to mimic and amplify, with the power of computation, this ability. The conceptual leap can pave the ground to a new trend of techniques, which can be variously instantiated from the proposed framework, by exploiting the numerous tools for causal discovery and inference. Preliminary results reported in this paper are promising.

Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to quantum speedups in optimization relies on the quantum acceleration of intermediate steps of classical algorithms, while keeping the overall algorithmic trajectory and solution quality unchanged. We propose Quantum Hamiltonian Descent (QHD), which is derived from the path integral of dynamical systems referring to the continuous-time limit of classical gradient descent algorithms, as a truly quantum counterpart of classical gradient methods where the contribution from classically-prohibited trajectories can significantly boost QHD's performance for non-convex optimization. Moreover, QHD is described as a Hamiltonian evolution efficiently simulatable on both digital and analog quantum computers. By embedding the dynamics of QHD into the evolution of the so-called Quantum Ising Machine (including D-Wave and others), we empirically observe that the D-Wave-implemented QHD outperforms a selection of state-of-the-art gradient-based classical solvers and the standard quantum adiabatic algorithm, based on the time-to-solution metric, on non-convex constrained quadratic programming instances up to 75 dimensions. Finally, we propose a "three-phase picture" to explain the behavior of QHD, especially its difference from the quantum adiabatic algorithm.

Mctx is a library with a JAX-native implementation of Monte Carlo tree search (MCTS) algorithms such as AlphaZero, MuZero, and Gumbel MuZero. For computation speed up, the implementation fully supports JIT-compilation. Search algorithms in Mctx are defined for and operate on batches of inputs, in parallel. This allows to make the most of the accelerators and enables the algorithms to work with large learned environment models parameterized by deep neural networks. Learning and search have been important topics since the early days of AI research.

Search-based agents: These agents use search algorithms to find solutions to problems. For example, a search-based agent might use algorithms like breadth-first search or A* to find the shortest path from one location to another. Planning agents: These agents use planning algorithms to determine the steps necessary to achieve a specific goal. For example, a robot equipped with a planning agent might use a planning algorithm to determine the sequence of actions necessary to pick up an object and place it in a specific location. Reasoning agents: These agents use reasoning and logic to solve problems.

For combinatorial optimization problems, model-based approaches such as mixed-integer programming (MIP) and constraint programming (CP) aim to decouple modeling and solving a problem: the 'holy grail' of declarative problem solving. We propose domain-independent dynamic programming (DIDP), a new model-based paradigm based on dynamic programming (DP). While DP is not new, it has typically been implemented as a problem-specific method. We propose Dynamic Programming Description Language (DyPDL), a formalism to define DP models, and develop Cost-Algebraic A* Solver for DyPDL (CAASDy), a generic solver for DyPDL using state space search. We formalize existing problem-specific DP and state space search methods for combinatorial optimization problems as DP models in DyPDL. Using CAASDy and commercial MIP and CP solvers, we experimentally compare the DP models with existing MIP and CP models, showing that, despite its nascent nature, CAASDy outperforms MIP and CP on a number of common problem classes.