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.

Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: Adaptive Staircase Policy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP.

Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost. Consequently, much effort has been made in the past decades to develop vehicle routing heuristics. In this article, we systematically survey the existing vehicle routing heuristics, particularly on works carried out in recent years. A classification of vehicle routing heuristics is presented, followed by a review of their methodologies, recent developments, and applications. Moreover, we present a general framework of state-of-the-art methods and provide insights into their success. Finally, three emerging research topics with notable works and future directions are discussed.