We present AutoTuneX, a system architecture design and implementation for users to interactively fine-tune large language models (LLMs) based on automated hyperparameter optimization particularly built around Bandit Limited Discrepancy Search. Next to a classical Graphical User Interface (GUI) our system features an agentic runtime to facilitate automated fine-tuning via chat.

Javier Carnerero-Cano, Massimiliano Pronesti, Radu Marinescu, Tigran T. Tchrakian, James Barry, Jasmina Gajcin, Yufang Hou, Alessandra Pascale, Elizabeth M. Daly. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Risk-averse Constrained Reinforcement Learning (RaCRL) aims to learn policies that minimise the likelihood of rare and catastrophic constraint violations caused by an environment’s inherent randomness. In general, risk-aversion leads to conservative exploration of the environment which typically results in converging to sub-optimal policies that fail to adequately maximise reward or, in some cases, fail to achieve the goal. In this paper, we propose an exploration-based approach for RaCRL called Optimistic Risk-averse Actor Critic (ORAC), which constructs an exploratory policy by maximising a local upper confidence bound of the state-action reward value function whilst minimising a local lower confidence bound of the risk-averse state-action cost value function. Specifically, at each step, the weighting assigned to the cost value is increased or decreased if it exceeds or falls below the safety constraint value. This way the policy is encouraged to explore uncertain regions of the environment to discover high reward states whilst still satisfying the safety constraints. Our experimental results demonstrate that the ORAC approach prevents convergence to sub-optimal policies and improves significantly the reward-cost trade-off in various continuous control tasks such as Safety-Gymnasium and a complex building energy management environment CityLearn.

Estimating the confidence of large language model (LLM) outputs is essential for real-world applications requiring high user trust. Black-box uncertainty quantification (UQ) methods, relying solely on model API access, have gained popularity due to their practical benefits. In this paper, we examine the implicit assumption behind several UQ methods, which use generation consistency as a proxy for confidence-an idea we formalize as the consistency hypothesis. We introduce three mathematical statements with corresponding statistical tests to capture variations of this hypothesis and metrics to evaluate LLM output conformity across tasks. Our empirical investigation, spanning 8 benchmark datasets and 3 tasks (question answering, text summarization, and text-to-SQL), highlights the prevalence of the hypothesis under different settings. Among the statements, we highlight the ‘Sim-Any’ hypothesis as the most actionable, and demonstrate how it can be leveraged by proposing data-free black-box UQ methods that aggregate similarities between generations for confidence estimation. These approaches can outperform the closest baselines, showcasing the practical value of the empirically observed consistency hypothesis.

Retrieval-augmented generation (RAG) has emerged as a promising solution to mitigate the limitations of large language models (LLMs), such as hallucinations and outdated information. However, it remains unclear how LLMs handle knowledge conflicts arising from different augmented retrieved passages, especially when these passages originate from the same source and have equal trustworthiness. In this work, we conduct a comprehensive evaluation of LLM-generated answers to questions that have varying answers based on contradictory passages from Wikipedia, a dataset widely regarded as a high-quality pre-training resource for most LLMs. Specifically, we introduce WikiContradict, a benchmark consisting of 253 high-quality, human-annotated instances designed to assess the performance of LLMs in providing a complete perspective on conflicts from the retrieved documents, rather than choosing one answer over another, when augmented with retrieved passages containing real-world knowledge conflicts. We benchmark a diverse range of both closed and open-source LLMs under different QA scenarios, including RAG with a single passage, and RAG with 2 contradictory passages. Through rigorous human evaluations on a subset of WikiContradict instances involving 5 LLMs and over 3,500 judgements, we shed light on the behaviour and limitations of these models. For instance, when provided with two passages containing contradictory facts, all models struggle to generate answers that accurately reflect the conflicting nature of the context, especially for implicit conflicts requiring reasoning. Since human evaluation is costly, wealso introduce an automated model that estimates LLM performance using a strong open-source language model, achieving an F-score of 0.8. Using this automated metric, we evaluate more than 1,500 answers from seven LLMs across all WikiContradict instances.

Logical Credal Networks or LCNs were recently introduced as a powerful probabilistic logic framework for representing and reasoning with imprecise knowledge. Unlike many existing formalisms, LCNs have the ability to represent cycles and allow specifying marginal and conditional probability bounds on logic formulae which may be important in many realistic scenarios. Previous work on LCNs has focused exclusively on marginal inference, namely computing posterior lower and upper probability bounds on a query formula. In this paper, we explore abductive reasoning tasks such as solving MAP and Marginal MAP queries in LCNs given some evidence. We first formally define the MAP and Marginal MAP tasks for LCNs and subsequently show how to solve these tasks exactly using search-based approaches. We then propose several approximate schemes that allow us to scale MAP and Marginal MAP inference to larger problem instances. An extensive empirical evaluation demonstrates the effectiveness of our algorithms on both random LCN instances as well as LCNs derived from more realistic use-cases.

A well-defined reward function is crucial for successful training of an reinforcement learning (RL) agent. However, defining a suitable reward function is a notoriously challenging task, especially in complex, multi-objective environments. Developers often have to resort to starting with an initial, potentially misspecified reward function, and iteratively adjusting its parameters, based on observed learned behavior. In this work, we aim to automate this process by proposing ITERS, an iterative reward shaping approach using human feedback for mitigating the effects of a misspecified reward function. Our approach allows the user to provide trajectory-level feedback on agent’s behavior during training, which can be integrated as a reward shaping signal in the following training iteration. We also allow the user to provide explanations of their feedback, which are used to augment the feedback and reduce user effort and feedback frequency. We evaluate ITERS in three environments and show that it can successfully correct misspecified reward functions.

The Logical Credal Network or LCN is a recent probabilistic logic designed for effective aggregation and reasoning over multiple sources of imprecise knowledge. An LCN specifies a set of probability distributions over all interpretations of a set of logical formulas for which marginal and conditional probability bounds on their truth values are known. Inference in LCNs involves the exact solution of a non-convex non-linear program defined over an exponentially large number of non-negative real valued variables and, therefore, is limited to relatively small problems. In this paper, we present ARIEL -- a novel iterative message-passing scheme for approximate inference in LCNs. Inspired by classical belief propagation for graphical models, our method propagates messages that involve solving considerably smaller local non-linear programs. Experiments on several classes of LCNs demonstrate clearly that ARIEL yields high quality solutions compared with exact inference and scales to much larger problems than previously considered.

Using reinforcement learning for automated theorem proving has recently received much attention. Current approaches use representations of logical statements that often rely on the names used in these statements and, as a result, the models are generally not transferable from one domain to another. The size of these representations and whether to include the whole theory or part of it are other important decisions that affect the performance of these approaches as well as their runtime efficiency. In this paper, we present NIAGRA; an ensemble Name InvAriant Graph RepresentAtion. NIAGRA addresses this problem by using 1) improved Graph Neural Networks for learning name-invariant formula representations that is tailored for their unique characteristics and 2) an efficient ensemble approach for automated theorem proving. Our experimental evaluation shows state-of-the-art performance on multiple datasets from different domains with improvements up to 10% compared to the best learning-based approaches. Furthermore, transfer learning experiments show that our approach significantly outperforms other learning-based approaches by up to 28%.

We present AutoDOViz, an interactive user interface for automated decision optimization (AutoDO) using reinforcement learning (RL). Decision optimization (DO) has classically being practiced by dedicated DO researchers [43] where experts need to spend long periods of time fine tuning a solution through trial-and-error. AutoML pipeline search has sought to make it easier for a data scientist to find the best machine learning pipeline by leveraging automation to search and tune the solution. More recently, these advances have been applied to the domain of AutoDO [36], with a similar goal to find the best reinforcement learning pipeline through algorithm selection and parameter tuning. However, Decision Optimization requires significantly more complex problem specification when compared to an ML problem. AutoDOViz seeks to lower the barrier of entry for data scientists in problem specification for reinforcement learning problems, leverage the benefits of AutoDO algorithms for RL pipeline search and finally, create visualizations and policy insights in order to facilitate the typical interactive nature when communicating problem formulation and solution proposals between DO experts and domain experts. In this paper, we report our findings from semi-structured expert interviews with DO practitioners as well as business consultants, leading to design requirements for human-centered automation for DO with RL. We evaluate a system implementation with data scientists and find that they are significantly more open to engage in DO after using our proposed solution. AutoDOViz further increases trust in RL agent models and makes the automated training and evaluation process more comprehensible. As shown for other automation in ML tasks [33, 59], we also conclude automation of RL for DO can benefit from user and vice-versa when the interface promotes human-in-the-loop.

Credal networks extend Bayesian networks to allow for imprecision in probability values. Marginal MAP is a widely applicable mixed inference task that identifies the most likely assignment for a subset of variables (called MAP variables). However, the task is extremely difficult to solve in credal networks particularly because the evaluation of each complete MAP assignment involves exact likelihood computations (combinatorial sums) over the vertices of a complex joint credal set representing the space of all possible marginal distributions of the MAP variables. In this paper, we explore Credal Marginal MAP inference and develop new exact methods based on variable elimination and depth-first search as well as several approximation schemes based on the mini-bucket partitioning and stochastic local search. An extensive empirical evaluation demonstrates the effectiveness of our new methods on random as well as real-world benchmark problems.

Scientific computing has experienced a surge empowered by advancements in technologies such as neural networks. However, certain important tasks are less amenable to these technologies, benefiting from innovations to traditional inference schemes. One such task is protein re-design. Recently a new re-design algorithm, {AOBB-K\textsuperscript{*}}, was introduced and was competitive with state-of-the-art {BBK\textsuperscript{*}} on small protein re-design problems. However, {AOBB-K\textsuperscript{*}} did not scale well. In this work, we focus on scaling up {AOBB-K\textsuperscript{*}} and introduce three new versions: {AOBB-K\textsuperscript{*}}-b (boosted), {AOBB-K\textsuperscript{*}}-{DH} (with dynamic heuristics), and {AOBB-K\textsuperscript{*}}-{UFO} (with underflow optimization) that significantly enhance scalability.

Optimizing a machine learning (ML) pipeline has been an important topic of AI and ML. Despite recent progress, pipeline optimization remains a challenging problem, due to potentially many combinations to consider as well as slow training and validation. We present the BLDS algorithm for optimized algorithm selection (ML operations) in a fixed ML pipeline structure. BLDS performs multi-fidelity optimization for selecting ML algorithms trained with smaller computational overhead, while controlling its pipeline search based on multi-armed bandit and limited discrepancy search. Our experiments on well-known classification benchmarks show that BLDS is superior to competing algorithms. We also combine BLDS with hyperparameter optimization, empirically showing the advantage of BLDS.

We introduce Logical Credal Networks (or LCNs for short) -- an expressive probabilistic logic that generalizes prior formalisms that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds on logic formulas, an LCN specifies a set of probability distributions over all its interpretations. Our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. We also define a generalized Markov condition that allows us to identify implicit independence relations between atomic formulas. We evaluate our method on benchmark problems such as random networks, Mastermind games with uncertainty and credit card fraud detection. Our results show that the LCN outperforms existing approaches; its advantage lies in aggregating multiple sources of imprecise information.

Most people associate the term `hedging' exclusively with financial applications, particularly the use of financial derivatives. We argue that hedging is an activity that human and machine agents should engage in more broadly, even when the agent's value is not necessarily in monetary units. In this paper, we propose a decision-theoretic view of hedging based on augmenting a probabilistic graphical model -- specifically a Bayesian network or an influence diagram -- with a reward. Hedging is therefore posed as a particular kind of graph manipulation, and can be viewed as analogous to control/intervention and information gathering related analysis. Effective hedging occurs when a risk-averse agent finds opportunity to balance uncertain rewards in their current situation. We illustrate the concepts with examples and counter-examples, and conduct experiments to demonstrate the properties and applicability of the proposed computational tools that enable agents to proactively identify potential hedging opportunities in real-world situations.

The importance of designing proteins, such as high affinity antibodies, has become ever more apparent. Computational Protein Design can cast such design problems as optimization tasks with the objective of maximizing K*, an approximation of binding affinity. Here we lay out a graphical model framework for K* optimization that enables use of compact AND/OR search algorithms. We designed an AND/OR branch-and-bound algorithm, AOBB-K*, for optimizing K* that is guided by a new K* heuristic and can incorporate specialized performance improvements with theoretical guarantees. As AOBB-K* is inspired by algorithms from the well studied task of Marginal MAP, this work provides a foundation for harnessing advancements in state-of-the-art mixed inference schemes and adapting them to protein design.

Influence diagrams (IDs) are graphical models for representing and reasoning with sequential decision-making problems under uncertainty. Limited memory influence diagrams (LIMIDs) model a decision-maker (DM) who forgets the history in the course of making a sequence of decisions. The standard inference task in IDs and LIMIDs is to compute the maximum expected utility (MEU), which is one of the most challenging tasks in graphical models. We present a model decomposition framework in both IDs and LIMIDs, which we call submodel decomposition that generates a tree of single-stage decision problems through a tree clustering scheme. We also develop a valuation algebra over the submodels that leads to a hierarchical message passing algorithm that propagates conditional expected utility functions over a submodel-tree as external messages. We show that the overall complexity is bounded by the maximum tree-width over the submodels, common in graphical model algorithms. Finally, we present a new method for computing upper bounds over a submodel-tree by first exponentiating the utility functions yielding a standard probabilistic graphical model as an upper bound and then applying standard variational upper bounds for the marginal MAP inference, yielding tighter upper bounds compared with state-of-the-art bounding schemes for the MEU task.

Influence diagrams provide a modeling and inference framework for sequential decision problems, representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables. Computing the maximum expected utility (MEU) and the optimizing policy is exponential in the constrained induced width and therefore is notoriously difficult for larger models. In this paper, we develop a new bounding scheme for MEU that applies partitioning based approximations on top of the decomposition scheme called a multi-operator cluster DAG for influence diagrams that is more sensitive to the underlying structure of the model than the classical join-tree decomposition of influence diagrams. Our bounding scheme utilizes a cost-shifting mechanism to tighten the bound further. We demonstrate the effectiveness of the proposed scheme on various hard benchmarks.

AutoML automatically selects, composes and parameterizes machine learning algorithms into a workflow or pipeline of operations that aims at maximizing performance on a given dataset. Although current methods for AutoML achieved impressive results they mostly concentrate on optimizing fixed linear workflows. In this paper, we take a different approach and focus on generating and optimizing pipelines of complex directed acyclic graph shapes. These complex pipeline structure may lead to discovering hidden features and thus boost performance considerably. We explore the power of heuristic search and context-free grammars to search and optimize these kinds of pipelines. Experiments on various benchmark datasets show that our approach is highly competitive and often outperforms existing AutoML systems.

The creation of Bayesian networks often requires the specification of a large number of parameters, making it highly desirable to be able to learn these parameters from historical data. In many cases, such data has uncertainty associated with it, including cases in which this data comes from unstructured analysis or from sensors. When creating diagnosis networks, for example, unstructured analysis algorithms can be run on the historical text descriptions or images of previous cases so as to extract data for learning Bayesian network parameters, but such derived data has inherent uncertainty associated with it due to the nature of such algorithms. Because of the inability of current Bayesian network parameter learning algorithms to incorporate such uncertainty, common approaches either ignore this uncertainty, thus reducing the resulting accuracy, or completely disregard such data. We present an approach for learning Bayesian network parameters that explicitly incorporates such uncertainty, and which is a natural extension of the Bayesian network formalism. We present a generalization of the Expectation Maximization parameter learning algorithm that enables it to handle any historical data with likelihood-evidence-based uncertainty, as well as an empirical validation demonstrating the improved accuracy and convergence enabled by our approach. We also prove that our extended algorithm maintains the convergence and correctness properties of the original EM algorithm, while explicitly incorporating data uncertainty in the learning process.

Finding a shortest path in a graph is at the core of many combinatorial search problems. A closely related problem refers to counting the number of shortest paths between two nodes. Such problems are solvable in polynomial time in the size of the graph. However, more realistic problem formulations could additionally specify constraints to satisfy. We study the problem of counting the shortest paths that are vertex disjoint and can satisfy additional constraints. Specifically, we look at the problems of counting vertex-disjoint shortest paths in edge-colored graphs, counting vertex-disjoint shortest paths with directional constraints, and counting vertex-disjoint shortest paths between multiple source-target pairs. We give a detailed theoretical analysis, and show formally that all of these three counting problems are NP-complete in general.

An influence diagram is a graphical representation of sequential decision-making under uncertainty, defining a structured decision problem by conditional probability functions and additive utility functions over discrete state and action variables. The task of finding the maximum expected utility of influence diagrams is closely related to the cost-optimal probabilistic planning, stochastic programmings, or model-based reinforcement learning. In this position paper, we address the heuristic search for solving influence diagram, where we generate admissible heuristic functions from graph decomposition schemes. Then, we demonstrate how such heuristics can guide an AND/OR branch and bound search. Finally, we briefly discuss the future directions for improving the quality of heuristic functions and search strategies.

Computing cycle-free solutions in cyclic AND/OR search spaces is an important AI problem. Previous work on optimal depth-first search strongly assumes the use of consistent heuristics, the need to keep all examined states in a transposition table, and the existence of solutions. We give a new theoretical analysis under relaxed assumptions where previous results no longer hold. We then present a generic approachto proving unsolvability, and apply it to RBFAOO and BLDFS, two state-of-the-art algorithms. We demonstrate the performance in domain-independent nondeterministic planning

We introduce #opt, a new inference task for graphical models which calls for counting the number of optimal solutions of the model. We describe a novel variable elimination based approach for solving this task, as well as a depth-first branch and bound algorithm that traverses the AND/OR search space of the model. The key feature of the proposed algorithms is that their complexity is exponential in the induced width of the model only. It does not depend on the actual number of optimal solutions. Our empirical evaluation on various benchmarks demonstrates the effectiveness of the proposed algorithms compared with existing depth-first and best-first search based approaches that enumerate explicitly the optimal solutions.

The Marginal MAP inference task is known to be extremely hard particularly because the evaluation of each complete MAP assignment involves an exact likelihood computation (a combinatorial sum). For this reason, most recent state-of-the-art solvers that focus on computing anytime upper and lower bounds on the optimal value are limited to solving instances with tractable conditioned summation subproblems. In this paper, we develop new search-based bounding schemes for Marginal MAP that produce anytime upper and lower bounds without performing exact likelihood computations. The empirical evaluation demonstrates the effectiveness of our new methods against the current best-performing search-based bounds.

It is well known that the problems of stochastic planning and probabilistic inference are closely related. This paper makes two contributions in this context. The first is to provide an analysis of the recently developed SOGBOFA heuristic planning algorithm that was shown to be effective for problems with large factored state and action spaces. It is shown that SOGBOFA can be seen as a specialized inference algorithm that computes its solutions through a combination of a symbolic variant of belief propagation and gradient ascent. The second contribution is a new solver for Marginal MAP (MMAP) inference. We introduce a new reduction from MMAP to maximum expected utility problems which are suitable for the symbolic computation in SOGBOFA. This yields a novel algebraic gradient-based solver (AGS) for MMAP. An experimental evaluation illustrates the potential of AGS in solving difficult MMAP problems.

Quantum circuit compilation (QCC) is an important problem in the emerging field of quantum computing. The problem has a strong relevance to combinatorial search, as solving approaches recently published include constraint programming and temporal planning. In this paper, we focus on a complexity analysis of quantum circuit compilation. We formulate a makespan optimization problem based on QCC, and prove that the problem is NP-complete. To the best of our knowledge, this is the first study on the theoretical complexity of QCC.

Mixed inference such as the marginal MAP query (some variables marginalized by summation and others by maximization) is key to many prediction and decision models. It is known to be extremely hard; the problem is NPPP-complete while the decision problem for MAP is only NP-complete and the summation problem is #P-complete. Consequently, approximation anytime schemes are essential. In this paper, we show that the framework of heuristic AND/OR search, which exploits conditional independence in the graphical model, coupled with variational-based mini-bucket heuristics can be extended to this task and yield powerful state-of-the-art schemes. Specifically, we explore the complementary properties of best-first search for reducing the number of conditional sums and providing time-improving upper bounds, with depth-first search for rapidly generating and improving solutions and lower bounds. We show empirically that a class of solvers that interleaves depth-first with best-first schemes emerges as the most competitive anytime scheme.

We introduce new anytime search algorithms that combine best-first with depth-first search into hybrid schemes for Marginal MAP inference in graphical models. The main goal is to facilitate the generation of upper bounds (via the best-first part) alongside the lower bounds of solutions (via the depth-first part) in an anytime fashion. We compare against two of the best current state-of-the-art schemes and show that our best+depth search scheme produces higher quality solutions faster while also producing a bound on their accuracy, which can be used to measure solution quality during search. An extensive empirical evaluation demonstrates the effectiveness of our new methods which enjoy the strength of best-first (optimality of search) and of depth-first (memory robustness), leading to solutions for difficult instances where previous solvers were unable to find even a single solution.

The formalism of multi-objective influence diagrams has recently been developed for modeling and solving sequential decision problems under uncertainty and multiple objectives. Since utility values representing the decision maker's preferences are only partially ordered (e.g., by the Pareto order) we no longer have a unique maximal value of expected utility, but a set of them. Computing the set of maximal values of expected utility and the corresponding policies can be computationally very challenging. In this paper, we consider alternative notions of optimality, one of the most important one being the notion of possibly optimal, namely optimal in at least one scenario compatible with the inter-objective tradeoffs. We develop a variable elimination algorithm for computing the set of possibly optimal expected utility values, prove formally its correctness, and compare variants of the algorithm experimentally.

Optimal heuristic search has been successful in many domains, including journey planning, route planning and puzzle solving. Existing work typically assumes that the cost of each action can easily be obtained. However, in many problems, the exact edge cost is expensive to compute. Existing search algorithms face a significant performance bottleneck, due to an excessive overhead associated with dynamically calculating exact edge costs. We present DEA*, an algorithm for problems with expensive edge cost computations. DEA* combines heuristic edge cost evaluations with delayed node expansions, reducing the number of exact edge computations. We formally prove that DEA* is optimal and it is efficient with respect to the number of exact edge cost computations. We empirically evaluate DEA* on multiple-worker routing problems where the exact edge cost is calculated by invoking an external multi-modal journey planning engine. The results demonstrate the effectiveness of our ideas in reducing the computational time and improving the solving ability. In addition, we show the advantages of DEA* in domain-independent planning, where we simulate that accurate edge costs are expensive to compute.

This paper explores the anytime performance of search-based algorithms for solving the Marginal MAP task over graphical models. The current state of the art for solving this challenging task is based on best-first search exploring the AND/OR graph with the guidance of heuristics based on mini-bucket and variational cost-shifting principles. Yet, those schemes are uncompromising in that they solve the problem exactly, or not at all, and often suffer from memory problems. In this work, we explore the well known principle of weighted search for converting best-first search solvers into anytime schemes. The weighted best-first search schemes report a solution early in the process by using inadmissible heuristics, and subsequently improve the solution. While it was demonstrated recently that weighted schemes can yield effective anytime behavior for pure MAP tasks, Marginal MAP is far more challenging (e.g., a conditional sum must be evaluated for every solution). Yet, in an extensive empirical analysis we show that weighted schemes are indeed highly effective for Marginal MAP yielding the most competitive schemes to date for this task.

This paper presents parallel dovetailing in a distributed-memory environment for exact MAP inference in graphical models. Parallel dovetailing is a simple procedure which performs multiple searches in parallel with different parameter configurations. We evaluate empirically the performance of parallel dovetailing with three state-of-the-art AND/OR search algorithms in solving various MAP inference benchmarks. Our results clearly show that parallel dovetailing is effective, yielding considerable speedups and improving the solving abilities of these state-of-the-art baseline methods.

The paper focuses on finding the m best solutions to combinatorial optimization problems using best-first or depth-first branch and bound search. Specifically, we present a new algorithm m-A*, extending the well-known A* to the m-best task, and for the first time prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since best-first algorithms require extensive memory, we also extend the memory-efficient depth-first branch and bound to the m-best task. We adapt both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments confirm theory that the best-first approach is largely superior when memory is available, but depth-first branch and bound is more robust. We also show that our algorithms are competitive with related schemes recently developed for the m-best task.

The paper presents and evaluates the power of parallel search for exact MAP inference in graphical models. We introduce a new parallel shared-memory recursive best-first AND/OR search algorithm, called SPRBFAOO, that explores the search space in a best-first manner while operating with restricted memory. Our experiments show that SPRBFAOO is often superior to the current state-of-the-art sequential AND/OR search approaches, leading to considerable speed-ups (up to 7-fold with 12 threads), especially on hard problem instances.

Recommender systems can be employed to assist users in complex decision making processes. This paper presents a multi-criteria housing recommender system which takes into account not just features of a home, such as rent, but also the transportation links to user specified locations. First, we describe an efficient multi-hop journey time calculator. Second, we introduce a mechanism to find the optimal solutions for multi-criteria evaluation, where a balanced trade-off between the target goals is found. Finally, we present a user study to demonstrate the potential of such a system.

Weighted search was explored significantly in recent years for path-finding problems, but until now was barely considered for optimization tasks such as MPE/MAP and Weighted CSPs. An important virtue of weighted search schemes, especially in the context of anytime search, is that they are w-optimal, i.e. when terminated, they return a weight w, and a solution cost C, such that C ≤ w · C*, where C* is the optimal cost. In this paper we introduce Weighted Branch and Bound (WBB) for graphical models and provide a broad empirical evaluation of its performance compared with one of the best unweighted anytime search scheme, BRAOBB (won Pascal 2011 competition). We also compare against weighted best-first (WBF). Our results show that W BB can be superior to both unweighted BB and to weighted BF on a significant number of instances. We also illustrate the benefit of weighted search in providing suboptimality relative error bounds.

The paper focuses on finding the m best solutions to combinatorial optimization problems using Best-First or Branchand- Bound search. Specifically, we present m-A*, extending the well-known A* to the m-best task, and prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since Best-First algorithms have memory problems, we also extend the memoryefficient Depth-First Branch-and-Bound to the m-best task. We extend both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments with 5 variants of Best-First and Branch-and-Bound confirm that Best-First is largely superior when memory is available, but Branch-and-Bound is more robust, while both styles of search benefit greatly when the heuristic evaluation function has increased accuracy.

In this paper we present and evaluate the power of best-first search over AND/OR search spaces for multi-objective constraint optimization. The main virtue of the AND/OR representation of the search space is its sensitivity to problem structure, which can translate into significant time savings. We introduce a linear-space best-first search algorithm that explores an AND/OR search tree and uses a class of partitioning-based heuristics for guidance. The superiority of the best-first approach over depth-first AND/OR Branch-and-Bound search using the same heuristic function is demonstrated empirically on random and real-world benchmarks for multi-objective constraint optimization.

The recently introduced notion of hypertree width has been shown to provide a broader characterization of tractable constraint and probabilistic networks than the tree width. This paper demonstrates empirically that in practice the bounding power of the tree width is still superior to the hypertree width for many benchmark instances of both probabilistic and deterministic networks.

Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment Multi-Valued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR Multi-Valued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is search-based, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inference-based and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs.