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Optimization Modulo Nonlinear Real Arithmetic, abbreviated as OMT(NRA), generally focuses on optimizing a given objective subject to quantifier-free Boolean combinations of primitive constraints, including Boolean variables, polynomial equations, and inequalities. It is widely applicable in areas like program verification, analysis, planning, and so on. The existing solver, OptiMathSAT, officially supporting OMT(NRA), employs an incomplete algorithm. We present a sound and complete algorithm, Optimization Cylindrical Algebraic Covering (OCAC), integrated within the Conflict-Driven Clause Learning (CDCL) framework, specifically tailored for OMT(NRA) problems. We establish the correctness and termination of CDCL(OCAC) and explore alternative approaches using cylindrical algebraic decomposition (CAD) and first-order formulations. Our work includes the development of the first complete OMT solver for NRA, demonstrating significant performance improvements. In benchmarks generated from SMT-LIB instances, our algorithm finds the optimum value in about 150\% more instances compared to the current leading solver, OptiMathSAT.

AAAI 2025

A Complete Algorithm for Optimization Modulo Nonlinear Real Arithmetic

constraint optimization

We are pleased to announce the Thirty-Ninth AAAI Conference on Artificial Intelligence (AAAI-25), which will be held in Philadelphia, Pennsylvania at the Pennsylvania Convention Center from February 25 to March 4, 2025.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-25 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.

### [Invited Speakers](https://aaai.org/conference/aaai/aaai-25/aaai-25-invited-speakers/)

Register [here](https://aaai.org/conference/aaai/aaai-25/registration/)

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-25 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.



technical paper

Coalition formation concerns autonomous agents that strategically interact to form self-organized coalitions. When agents lack initial sufficient information to evaluate their preferences before interacting with others, they learn them online through repeated feedback while iteratively forming coalitions. In this work, we introduce online learning in coalition formation from a non-cooperative perspective, studying the impact of collective data utilization where selfish agents aim to accelerate their learning by leveraging a shared data platform. Thus, the efficiency and dynamics of the learning process are affected by each agent's local feedbacks, motivating us to explore the tension between semi-bandit and bandit feedback, which differ in the granularity of utility information observed by each agent. Under our non-cooperative viewpoint, we evaluate the system by means of Nash stability, where no agent can improve her utility by unilaterally deviating. Our main result is a sample-efficient algorithm for selfish agents that aims to minimize their Nash regret under both semi-bandit and bandit feedback, implying approximately Nash stable outcomes. Under both feedback settings, our algorithm enjoys Nash regret and sample complexity bounds that are optimal up to logarithmic factors.

Online Learning of Coalition Structures by Selfish Agents

The MaxSAT problem is an optimization version of the satisfiability problem (SAT). A tight lower bound (LB) on the number of the falsified soft clauses in a MaxSAT solution is crucial for the efficiency of Branch-and-Bound (BnB) MaxSAT solvers. To compute LB, modern BnB solvers detect disjoint inconsistent subsets of soft clauses, called cores, using unit propagation. A notable feature in these solvers is that soft clauses belonging to already detected cores cannot be reused to detect additional cores, limiting the number of cores that can be detected. In this paper, we propose an unlocking mechanism that allows the reuse of soft clauses in already detected cores while ensuring the soundness of LB. Experimental results show that this unlocking mechanism consistently improves the performance of a state-of-the-art BnB solver.

Improving the Lower Bound in Branch-and-Bound Algorithms for MaxSAT

There are two manifestations of classification fairness. One is the preference for head classes with more instances due to the long-tail (LT) distribution of training data. The other is the clever Hans (CH) effect, where non-discriminative features are mistakenly used for classification. In this paper, we find that using category-agnostic zero-valued data can simultaneously reveal both types of unfairness. Based on this, we propose a zero uniformity training (ZUT) framework to optimize classification fairness. The ZUT framework inputs category-agnostic zero-valued data into the model in parallel and uses zero uniformity loss (ZUL) to optimize classification fairness. The ZUL loss mitigates bias towards specific classes by unifying the classification features corresponding to zero-valued data. The ZUT framework is compatible with various classification-based tasks. Experiments show that the ZUT framework can improve the performance of multiple state-of-the-art methods in image classification, person re-identification, and semantic segmentation.

Fair Training with Zero Inputs

Accurately predicting the trajectory of vehicles is critically important for ensuring safety and reliability in autonomous driving. Although considerable research efforts have been made recently, the inherent trajectory uncertainty caused by various factors including the dynamic driving intends and the diverse driving scenarios still poses significant challenges to accurate trajectory prediction. To address this issue, we propose C2F-TP, a coarse-to-fine denoising framework for uncertainty-aware vehicle trajectory prediction. C2F-TP features an innovative two-stage coarse-to-fine prediction process. Specifically, in the first stage, we propose a spatial-temporal interaction module to capture the inter-vehicle interactions and learn a multimodal trajectory distribution, from which a certain number of noisy trajectories are sampled. Next, in the trajectory refinement stage, we design a conditional denoising model to reduce the uncertainties of the sampled trajectories through a step-wise denoising operation. Extensive experiments are conducted on two real datasets NGSIM and highD that are widely adopted in trajectory prediction. The result demonstrates the effectiveness of our proposal. The code can be found at https://anonymous.4open.science/r/C2F-TP-1459.

C2F-TP: A Coarse-to-Fine Denoising Framework for Uncertainty-Aware Trajectory Prediction

Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities.
	In *robust* MDP (RMDP), every action is associated with an *uncertainty set* of probability distributions, modelling that transition probabilities are not known precisely.
	Based on the known theoretical connection to stochastic games, we provide a framework for solving RMDPs that is generic, reliable, and efficient.
	It is *generic* both with respect to the model, allowing for a wide range of uncertainty sets, including but not limited to intervals, $L^1$- or $L^2$-balls, and polytopes; and with respect to the objective, including long-run average reward, undiscounted total reward, and stochastic shortest path.
	It is *reliable*, as our approach not only converges in the limit, but provides precision guarantees at any time during the computation.
	It is *efficient* because -- in contrast to state-of-the-art approaches -- it avoids explicitly constructing the underlying stochastic game.
	Consequently, our prototype implementation outperforms existing tools by several orders of magnitude and can solve RMDPs with a million states in under a minute.

Solving Robust Markov Decision Processes: Generic, Reliable, Efficient

Multi-objective evolutionary algorithms (MOEAs) are widely used for searching optimal solutions in complex multi-component applications. Traditional MOEAs for multi-component deep learning (MCDL) systems face challenges in enhancing the search efficiency while maintaining the diversity. To combat these, this paper proposes $\mu$MOEA, the first LLM-empowered adaptive evolutionary search methodology to detect safety violations in MCDL systems. Inspired by the context-understanding ability of Large Language Models (LLMs), $\mu$MOEA promotes the LLM to comprehend the optimization problem and generate an initial population tailed to evolutionary objectives. Subsequently, it employs adaptive selection and variation techniques to iteratively produce offspring, balancing the evolutionary efficiency and diversity.
During the evolutionary process, to navigate away from the local optima,  $\mu$MOEA integrates the evolutionary experience back into the LLM. This utilization harnesses the LLM's quantitative reasoning prowess to generate differential seeds, breaking away from current optimal solutions. We evaluate the effectiveness of \name in finding safety violations of MCDL systems, and compare its performance with state-of-the-art MOEA methods. Experimental results show that \name can significantly improve the efficiency and diversity of the multi-objective evolutionary search.

An LLM-Empowered Adaptive Evolutionary Algorithm for Multi-Component Deep Learning Systems

As a long-term challenge and fundamental requirement in vision and language tasks, visual grounding aims to localize a target referred by a natural language query. The regional annotations form a superficial correlation between the subject of expression and some common visual entities, which hinder models from comprehending the linguistic content and structure. However, current one-stage methods struggle to uniformly model the visual and linguistic structure due to the structural gap between continuous image patches and discrete text tokens. In this paper, we propose a semi-structured reasoning framework for visual grounding to gradually comprehend the linguistic content and structure. Specifically, we devise a cross-modal content alignment module to effectively align unlabeled contextual information into a stable semantic space corrected by token-level prior knowledge obtained with CLIP. A multi-branch modulated localization module is also established to obtain modulation grounding by linguistic structure. Through a soft split mechanism, our method can destructure the expression into a fixed semi-structure (i.e., subject and context) while ensuring the completeness of linguistic content. Our method is thus capable of building a semi-structured reasoning system to effectively comprehend the linguistic content and structure by content alignment and structure modulated grounding. Experimental results on five widely-used datasets validate the performance improvements of our proposed method. Our code will be available soon.

Look Around Before Locating: Considering Content and Structure Information for Visual Grounding

Constrained Markov decision processes (CMDPs), in which the agent optimizes expected payoffs while keeping the expected cost below a given threshold, are the leading framework for safe sequential decision making under stochastic uncertainty. Among algorithms for planning and learning in CMDPs, methods based on Monte Carlo tree search (MCTS) have particular importance due to their efficiency and extendibility to more complex frameworks (such as partially observable settings and games). However, current MCTS-based methods for CMDPs either struggle with finding safe (i.e., constraint-satisfying) policies, or are too conservative and do not find valuable policies. We introduce Threshold UCT (T-UCT), an online MCTS-based algorithm for CMDP planning. Unlike previous MCTS-based CMDP planners, T-UCT explicitly estimates Pareto curves of cost-utility trade-offs throughout the search tree, using these together with a novel action selection and threshold update rule to seek safe and valuable policies. Our experiments demonstrate that our approach significantly outperforms state-of-the-art methods from the literature.

Threshold UCT: Cost-Constrained Monte Carlo Tree Search with Pareto Curves

Humans naturally rely on floor plans to navigate in unfamiliar environments because they are easy to access, consistently reliable, and rich in geometric detail. However, existing visual navigation settings neglect such informative prior knowledge, limiting the efficiency and accuracy. To eliminate this gap, we introduce a novel navigation task: Floor Plan Visual Navigation (FloNa), the first attempt to incorporate floor plan into the embodied visual navigation. Although the floor plan offers informative knowledge, two additional challenges arise: (1) how to map observed images and the floor plan sketch, given their different modalities, and (2) how to avoid collision with scene furniture that the floor plan does not depict. To address these issues, we propose FloDiff, a novel diffusion policy framework incorporating a localization module to facilitate the matching between the current observation and the floor plan. We further collect 20k navigation episodes from 117 scenes in the iGibson simulator to support the training and evaluation. The extensive experiments show the effectiveness and efficiency of our proposed framework in unfamiliar scenes using floor plan knowledge.

FloNa: Floor Plan Guided Embodied Visual Navigation

In multi-agent reinforcement learning, centralized training with decentralized execution (CTDE) methods typically assume that agents make decisions based on their local observations independently, which may not lead to a correlated joint policy with coordination. Coordination can be explicitly encouraged during training and individual policies can be trained to imitate the correlated joint policy. However, this may lead to an $\textit{asymmetric learning failure}$ due to the observation mismatch between the joint and individual policies. Inspired by the concept of correlated equilibrium, we introduce a $\textit{strategy modification}$ called AgentMixer that allows agents to correlate their policies. AgentMixer combines individual partially observable policies into a joint fully observable policy non-linearly. To enable decentralized execution, we introduce $\textit{Individual-Global-Consistency}$ to guarantee mode consistency during joint training of the centralized and decentralized policies and prove that AgentMixer converges to an $\epsilon$-approximate Correlated Equilibrium. In the Multi-Agent MuJoCo, SMAC-v2, Matrix Game, and Predator-Prey benchmarks, AgentMixer outperforms or matches state-of-the-art methods.

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Online Learning of Coalition Structures by Selfish Agents

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