RMSProp avoids both the vanishing and exploding gradient problems.

We study an efficient implementation of Multi-Armed Bandit (MAB)-based Monte-Carlo Tree Search (MCTS) for classical planning. One weakness of MCTS is that it spends a significant time deciding which node to expand next. While selecting a node from an OPEN list with $N$ nodes has $O(1)$ runtime complexity with traditional array-based priority-queues for dense integer keys, the tree-based OPEN list used by MCTS requires $O(\log N)$, which roughly corresponds to the search depth $d$. In classical planning, $d$ is arbitrarily large (e.g., $2^k-1$ in $k$-disk Tower-of-Hanoi) and the runtime for node selection is significant, unlike in game tree search, where the cost is negligible compared to the node evaluation (rollouts) because $d$ is inherently limited by the game (e.g., $d\leq 361$ in Go). To improve this bottleneck, we propose a bilevel modification to MCTS that runs a best-first search from each selected leaf node with an expansion budget proportional to $d$, which achieves amortized $O(1)$ runtime for node selection, equivalent to the traditional queue-based OPEN list. In addition, we introduce Tree Collapsing, an enhancement that reduces action selection steps and further improves the performance.

Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, reflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS research.

Ensuring responsible use of artificial intelligence (AI) has become imperative as autonomous systems increasingly influence critical societal domains. However, the concept of trustworthy AI remains broad and multi-faceted. This thesis advances knowledge in the safety, fairness, transparency, and accountability of AI systems. In safety, we extend classical deterministic shielding techniques to become resilient against delayed observations, enabling practical deployment in real-world conditions. We also implement both deterministic and probabilistic safety shields into simulated autonomous vehicles to prevent collisions with road users, validating the use of these techniques in realistic driving simulators. We introduce fairness shields, a novel post-processing approach to enforce group fairness in sequential decision-making settings over finite and periodic time horizons. By optimizing intervention costs while strictly ensuring fairness constraints, this method efficiently balances fairness with minimal interference. For transparency and accountability, we propose a formal framework for assessing intentional behaviour in probabilistic decision-making agents, introducing quantitative metrics of agency and intention quotient. We use these metrics to propose a retrospective analysis of intention, useful for determining responsibility when autonomous systems cause unintended harm. Finally, we unify these contributions through the ``reactive decision-making'' framework, providing a general formalization that consolidates previous approaches. Collectively, the advancements presented contribute practically to the realization of safer, fairer, and more accountable AI systems, laying the foundations for future research in trustworthy AI.

Many real-world scenarios require multiple agents to coordinate in shared environments, while balancing trade-offs between multiple, potentially competing objectives. Current multi-objective multi-agent path finding (MO-MAPF) algorithms typically produce conflict-free plans by computing Pareto frontiers. They do not explicitly optimize for user-defined preferences, even when the preferences are available, and scale poorly with the number of objectives. We propose a lexicographic framework for modeling MO-MAPF, along with an algorithm \textit{Lexicographic Conflict-Based Search} (LCBS) that directly computes a single solution aligned with a lexicographic preference over objectives. LCBS integrates a priority-aware low-level $A^*$ search with conflict-based search, avoiding Pareto frontier construction and enabling efficient planning guided by preference over objectives. We provide insights into optimality and scalability, and empirically demonstrate that LCBS computes optimal solutions while scaling to instances with up to ten objectives -- far beyond the limits of existing MO-MAPF methods. Evaluations on standard and randomized MAPF benchmarks show consistently higher success rates against state-of-the-art baselines, especially with increasing number of objectives.

Planning is one of the most critical tasks in autonomous systems, where even a small error can lead to major failures or million-dollar losses. Current state-of-the-art neural planning approaches struggle with complex domains, producing plans with missing preconditions, inconsistent goals, and hallucinations. While classical planners provide logical guarantees, they lack the flexibility and natural language understanding capabilities needed for modern autonomous systems. Existing neuro-symbolic approaches use one-shot translation from natural language to formal plans, missing the opportunity for neural and symbolic components to work and refine solutions together. To address this gap, we develop LOOP -- a novel neuro-symbolic planning framework that treats planning as an iterative conversation between neural and symbolic components rather than simple translation. LOOP integrates 13 coordinated neural features including graph neural networks for spatial relationships, multi-agent validation for consensus-based correctness, hierarchical decomposition for complex task management, and causal memory that learns from both successes and failures. Unlike existing approaches, LOOP generates PDDL specifications, refines them iteratively based on symbolic feedback, and builds a causal knowledge base from execution traces. LOOP was evaluated on six standard IPC benchmark domains, where it achieved 85.8% success rate compared to LLM+P (55.0%), LLM-as-Planner (19.2%), and Tree-of-Thoughts (3.3%). This work shows that the key to reliable planning is not in choosing between neural networks or symbolic reasoners but it lies in making them actually ``talk'' to each other during the entire process. LOOP provides a thorough blueprint for building autonomous systems that can finally be trusted with critical real-world applications.

Freeway is excluded from this table as Junyent et al. [ Epochs 8 Loss Function for Policy Categorical crossentropy Loss Function for Value Function Huber Discount factor used in TD Learning 0.99 Time steps between target network updates (for value network) 10,000 Interval size of learning schedule Due to computational restraints we could not tune the hyperparameters of N-CPL.

In over sixty years since its inception, the field of planning has made significant contributions to both the theory and practice of building planning software that can solve a never-before-seen planning problem. This was done through established practices of rigorous design and evaluation of planning systems. It is our position that this rigor should be applied to the current trend of work on planning with large language models. One way to do so is by correctly incorporating the insights, tools, and data from the automated planning community into the design and evaluation of LLM-based planners. The experience and expertise of the planning community are not just important from a historical perspective; the lessons learned could play a crucial role in accelerating the development of LLM-based planners. This position is particularly important in light of the abundance of recent works that replicate and propagate the same pitfalls that the planning community has encountered and learned from. We believe that avoiding such known pitfalls will contribute greatly to the progress in building LLM-based planners and to planning in general.

Recent work has shown that successful per-domain generalizing action policies can be learned. Scaling behavior, from small training instances to large test instances, is the key objective; and the use of validation instances larger than training instances is one key to achieve it. Prior work has used fixed validation sets. Here, we introduce a method generating the validation set dynamically, on the fly, increasing instance size so long as informative and feasible. We also introduce refined methodology for evaluating scaling behavior, generating test instances systematically to guarantee a given confidence in coverage performance for each instance size. In experiments, dynamic validation improves scaling behavior of GNN policies in all 9 domains used.