Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored. A fundamental problem is to count plans, which relates to the conditional probability on the plan space. Indeed, qualitative and quantitative approaches are well-established in various other areas of automated reasoning. We present the first study to quantitative and qualitative reasoning on the plan space. In particular, we focus on polynomially bounded plans. On the theoretical side, we study its complexity, which gives rise to rich reasoning modes. Since counting is hard in general, we introduce the easier notion of facets, which enables understanding the significance of operators. On the practical side, we implement quantitative reasoning for planning. Thereby, we transform a planning task into a propositional formula and use knowledge compilation to count different plans. This framework scales well to large plan spaces, while enabling rich reasoning capabilities such as learning pruning functions and explainable planning.
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Monte-Carlo Tree Search (MCTS) is a popular approach to online planning under uncertainty. While MCTS uses statistical sampling via multi-armed bandits to avoid exhaustive search in complex domains, common closed-loop approaches typically construct enormous search trees to consider a large number of potential observations and actions. On the other hand, open-loop approaches offer better memory efficiency by ignoring observations but are generally not competitive with closed-loop MCTS in terms of performance - even with commonly integrated human knowledge. In this paper, we propose Counterfactual Open-loop Reasoning with Ad hoc Learning (CORAL) for open-loop MCTS, using a causal multi-armed bandit approach with unobserved confounders (MABUC). CORAL consists of two online learning phases that are conducted during the open-loop search. In the first phase, observational values are learned based on preferred actions. In the second phase, counterfactual values are learned with MABUCs to make a decision via an intent policy obtained from the observational values. We evaluate CORAL in four POMDP benchmark scenarios and compare it with closed-loop and open-loop alternatives. In contrast to standard open-loop MCTS, CORAL achieves competitive performance compared with closed-loop algorithms while constructing significantly smaller search trees.
Language-conditioned robotic manipulation in unstructured environments presents significant challenges for intelligent robotic systems. However, due to partial observation or imprecise action prediction, failure may be unavoidable for learned policies. Moreover, operational failures can lead to the robotic arm entering an untrained state, potentially causing destructive results. Consequently, the ability to detect and self-correct failures is crucial for the development of practical robotic systems. To address this challenge, we propose a foresight-driven failure detection and self-correction module for robot manipulation. By leveraging 3D Gaussian Splatting, we represent the current scene with multiple Gaussians. Subsequently, we train a prediction network to forecast the Gaussian representation of future scenes conditioned on planned actions. Failure is detected when the predicted future significantly deviates from the real observation after action execution. In such cases, the end-effector rolls back to the previous action to avoid an untrained state. Integrating this approach with the PerACT framework, we develop a self-correcting robot manipulation policy. Evaluations on ten RLBench tasks with 166 variations demonstrate the superior performance of the proposed method, which outperforms state-of-the-art methods by 12.0% success rate on average.
Told You That Will Not Work: Optimal Corrections to Planning Domains Using Counter-Example Plans
PDF ↗Hardness of modeling a planning domain is a major obstacle for making automated planning techniques accessible. We developed a tool that helps modelers correct domains based on available information such as the known feasibility or infeasibility of certain plans. Designing model repair strategies that are capable of repairing flawed planning domains automatically has been explored in previous work to use positive plans (invalid in the given (flawed) domain but feasible in the ``true'' domain). In this work, we highlight the importance of and study counter-example negative plans (valid in the given (flawed) domain but infeasible in the ``true'' domain). Our approach automatically corrects a domain by finding an optimal repair set to the domain which turns all negative plans into non-solutions, in addition to making all positive plans solutions. Experiments indicate strong performance in the fast-downward benchmark suite with random errors. A handcrafted benchmark with domain flaws inspired by some practical applications also motivates the method's efficacy.
Formulating a real-world problem under the Reinforcement Learning framework involves non-trivial design choices, such as selecting a discount factor for the learning objective (dis- counted cumulative rewards), which articulates the planning horizon of the agent. This work investigates the impact of the discount factor on the bias-variance trade-off given structural parameters of the underlying Markov Decision Process. Our results support the idea that a shorter planning horizon might be beneficial, especially under partial observability.
One of the major techniques to tackle temporal planning problems is heuristic search augmented with a symbolic representation of time in the states. Augmenting the problem with composite actions (macro-actions) is a simple and powerful approach to create "shortcuts" in the search space, at the cost of augmenting the branching factor of the problem and thus the expansion time of a heuristic search planner. Hence, it is of paramount importance to select the right macro-actions and minimize the number of such actions to optimize the planner performance. In this paper, we first discuss a simple, yet powerful, model similar to macro-actions for the case of temporal planning, and we call these macro-events. Then, we present a novel ranking function to extract and select a suitable set of macro-events from a dataset of valid plans. In our ranking approach, we consider an estimation of the hypothetical search space for a blind search including a candidate set of macro-events under four different exploitation schemata. Finally, we experimentally demonstrate that the proposed approach yields a substantial performance improvement for a state-of-the-art temporal planner.
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.
There is an increasing body of work using Large Language Models (LLMs) as agents for orchestrating workflows and making decisions in domains that require planning and multistep reasoning. As a result, it is imperative to evaluate LLMs on core skills required for planning. In this work, we present ACPBench, a benchmark for evaluating the reasoning tasks in the field of planning. The benchmark consists of 7 reasoning tasks over 13 planning domains. The collection is constructed from planning domains described in a formal language. This allows us to synthesize problems with provably correct solutions across many tasks and domains. Further, it allows us the luxury of scale without additional human effort, i.e., many] additional problems can be created automatically. Our extensive evaluation of 21 LLMs and OpenAI o1 reasoning models highlight the significant gap in the reasoning capability of the LLMs. Our findings with OpenAI o1, a multi-turn reasoning model, reveal significant gains in performance on multiple-choice questions, yet surprisingly, no notable progress is made on boolean questions.
Large Language Models (LLMs) have shown promise in solving natural language-described planning tasks, but their direct use often leads to inconsistent reasoning and hallucination. While hybrid LLM-symbolic planning pipelines have emerged as a more robust alternative, they typically require extensive expert intervention to refine and validate generated action schemas. It not only limits scalability but also introduces a potential for biased interpretation, as a single expert's interpretation of ambiguous natural language descriptions might not align with the user's actual intent. To address this, we propose a novel approach that constructs an action schema library to generate multiple candidates, accounting for the diverse possible interpretations of natural language descriptions. We further introduce a semantic validation and ranking module that automatically filter and rank these candidates without expert-in-the-loop. The experiments showed our pipeline maintains superiority in planning over the direct LLM planning approach. These findings demonstrate the feasibility of a fully automated end-to-end LLM-symbolic planner that requires no expert intervention, opening up the possibility for a broader audience to engage with AI planning with less prerequisite of domain expertise.
The application of graph neural networks (GNNs) to learn heuristic functions in classical planning is gaining traction. Despite the variety of methods proposed in the literature to encode classical planning tasks for GNNs, a comparative study evaluating their relative performances has been lacking. Moreover, some encodings have been assessed solely for their expressiveness rather than practical effectiveness in planning. This paper provides an extensive comparative analysis of existing encodings. Our results indicate that the smallest encoding based on Gaifman graphs, not yet applied in planning, outperforms the rest due to its fast evaluation times and the informativeness of the resulting heuristic. The overall coverage measured on the IPC almost reaches that of the state-of-the-art planner LAMA while exhibiting rather complementary strengths across different domains.
Despite the widespread success of pattern database (PDB) heuristics in classical planning, to date there has been no application of PDBs to planning with numeric variables. In this paper we attempt to close this gap. We address optimal numeric planning involving conditions characterized by linear expressions and actions that modify numeric variables by constant quantities. Building upon prior research, we present an adaptation of PDB heuristics to numeric planning, introducing several approaches to deal with the unbounded nature of numeric variable projections. These approaches aim to restrict the initially infinite projections, thereby bounding the number of states and ultimately constraining the resulting PDBs. We show that the PDB heuristics obtained with our approach can provide strong guidance for the search.
Logistics and transportation networks require a large amount of resources to realise necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connections that are only available at specific times, intricate models are needed to portray them accurately. In this paper, we study the problem of minimizing the number of resources needed to realise a dynamic network, using the temporal graphs model. In a temporal graph, edges appear at specific points in time. Given a temporal graph and a natural number k, we ask whether we can cover every temporal edge exactly once using at most k temporal journeys; in a temporal journey consecutive edges have to adhere to the order of time. We conduct a thorough investigation of the complexity of the problem with respect to four dimensions: (a) whether the type of the temporal journey is a walk, a trail, or a path; (b) whether the chronological order of edges in the journey is strict or non-strict; (c) whether the temporal graph is directed or undirected; (d) whether the start and end points of each journey are given. We almost completely resolve the complexity of these problems and provide dichotomies for each of them with respect to k.
We consider temporal numeric planning problems Π expressed in PDDL2.1, and show how it is possible to produce SMT formulas (i) whose models correspond to valid plans of Π, and (ii) which extends the recently proposed planning with patterns approach from the numeric to the temporal case. We prove the correctness and completeness of the approach and that it outperforms all the publicly available temporal planners on 10 domains with required concurrency.
It is well known that numeric planning can be made decidable if the domain of all numeric state variables is finite. This bounded formulation can be polynomially compiled into classical planning with Boolean conditions and conditional effects preserving the plan size exactly. However, it remains unclear whether this compilation has any practical utility. To explore this aspect, this work revisits the theoretical compilation framework from a practical perspective, focusing on the fragment of simple numeric planning. Specifically, we introduce three different compilations. The first, called one-hot, aims to systematise the current practice among planning practitioners of modelling numeric planning through classical planning. The other two, termed binary compilations, extend and specialise the logarithmic encoding introduced in previous literature. Our experimental analysis reveals that the overly complex logarithmic encoding can, surprisingly, be made practical with some representational expedients. Among these, the use of axioms is particularly crucial. Furthermore, we identify a class of mildly numeric planning problems where a classical planner, i.e., LAMA, when run on the compiled problem, is highly competitive with state-of-the-art numeric planners.
We introduce PokerBench - a benchmark for evaluating the poker-playing abilities of large language models (LLMs). As LLMs excel in traditional NLP tasks, their application to complex, strategic games like poker poses a new challenge. Poker, an incomplete information game, demands a multitude of skills such as mathematics, reasoning, planning, strategy, and a deep understanding of game theory and human psychology. This makes Poker the ideal next frontier for large language models. PokerBench consists of a comprehensive compilation of 11,000 most important scenarios, split between pre-flop and post-flop play, developed in collaboration with trained poker players. We evaluate prominent models including GPT-4, ChatGPT 3.5, and various Llama and Gemma series models, finding that all state-of-the-art LLMs underperform in playing optimal poker. However, after fine-tuning, these models show marked improvements. We validate PokerBench by having models with different scores compete with each other, demonstrating that higher scores on PokerBench leads to higher win rates in actual poker games. Through gameplay between our fine-tuned model and GPT-4, we also identify limitations of simple supervised fine-tuning for learning optimal playing strategy, suggesting the need for more advanced methodologies for effectively training language models to excel in games. PokerBench thus presents a unique benchmark for a quick and reliable evaluation of the poker-playing ability of LLMs as well as a comprehensive benchmark to study the progress of LLMs in complex game-playing scenarios.
Encoder of Thoughts: Enhancing Planning Ability in Language Agents Through Structural Embedding
PDF ↗Large Language Models (LLMs), when combined with agent mechanisms, show great promise in applications requiring robust planning ability, such as financial analysis and medical diagnostics. However, the increasingly complex reasoning structures designed to enhance the planning ability of language agents often exceed the processing and comprehension capabilities of LLMs, thereby limiting their effectiveness. To address these challenges, we introduce the Encoder of Thoughts (EoT), a novel reasoning structure modeling method based on graph neural networks. EoT processes the reasoning structures of planning methods through a plug-and-play structural encoder and aligns these structural information with the input space of LLMs, enabling seamless integration with existing language agents. Experiments on multi-step reasoning and plan generation demonstrate that EoT significantly improves the performance of language agents. Moreover, EoT demonstrated stable results when combined with different LLMs and planning algorithms, further underscoring its potential for broader application.
For AI agents to be helpful to humans, they should be able to follow natural language instructions to complete everyday cooperative tasks in human environments. However, real human instructions inherently possess ambiguity, because the human speakers assume sufficient prior knowledge about their hidden goals and intentions. Standard language grounding and planning methods fail to address such ambiguities because they do not model human internal goals as additional partially observable factors in the environment. We propose a new framework, Follow Instructions with Social and Embodied Reasoning (FISER), aiming for better natural language instruction following in collaborative embodied tasks. Our framework makes explicit inferences about human goals and intentions as intermediate reasoning steps. We implement a set of Transformer-based models and evaluate them over a challenging benchmark, HandMeThat. We empirically demonstrate that using social reasoning to explicitly infer human intentions before making action plans surpasses purely end-to-end approaches. We also compare our implementation with strong baselines, including Chain of Thought prompting on the largest available pre-trained language models, and find that FISER provides better performance on the embodied social reasoning tasks under investigation, reaching the state-of-the-art on HandMeThat.
AI systems make decisions in physical environments through primitive actions or affordances that are accessed via API calls. While deploying AI agents in the real world involves numerous high-level actions, existing embodied simulators offer a limited set of domain-salient APIs. This naturally brings up the questions: how many primitive actions (APIs) are needed for a versatile embodied agent, and how should they look like? We explore this via a thought experiment: assuming that wikiHow tutorials cover a wide variety of human-written tasks, what is the space of APIs needed to cover these instructions? We propose a framework to iteratively induce new APIs by grounding wikiHow instruction to situated agent policies. Inspired by recent successes in large language models (LLMs) for embodied planning, we propose a few-shot prompting to steer GPT-4 to generate Pythonic programs as agent policies and bootstrap a universe of APIs by 1) reusing a seed set of APIs; and then 2) fabricate new API calls when necessary. The focus of this thought experiment is on defining these APIs rather than their excitability. We apply the proposed pipeline on instructions from wiki- How tutorials. On a small fraction (0.5%) of tutorials, we induce an action space of 300+ APIs necessary for capturing the rich variety of tasks in the physical world. A detailed automatic and human analysis of the induction output reveals that the proposed pipeline enables effective reuse and creation of APIs. Moreover, a manual review revealed that existing simulators support only a small subset of the induced APIs (9 of the top 50 frequent APIs), motivating the development of action-rich embodied environments.
Language Models of Code Are Few-Shot Planners and Reasoners for Multi-Document Summarization with Attribution
PDF ↗Document summarization has greatly benefited from advances in large language models (LLMs). In real-world situations, summaries often need to be generated from multiple documents with diverse sources and authors, lacking a clear information flow. Naively concatenating these documents and generating a summary can lead to poorly structured narratives and redundancy. Additionally, attributing each part of the generated summary to a specific source is crucial for reliability. In this study, we address multi-document summarization with attribution using our proposed solution ***MiDAS-PRo***, consisting of three stages: (i) Planning the hierarchical organization of source documents, (ii) Reasoning by generating relevant entities/topics, and (iii) Summary Generation. We treat the first two sub-problems as a code completion task for LLMs. By incorporating well-selected in-context learning examples through a graph attention network, LLMs effectively generate plans and reason topics for a document collection. Experiments on summarizing scientific articles from public datasets show that our approach outperforms state-of-the-art baselines in both automated and human evaluations.
VCR: A “Cone of Experience” Driven Synthetic Data Generation Framework for Mathematical Reasoning
PDF ↗Large language models (LLMs) have shown excellent performance in natural language processing but struggle with mathematical reasoning. As the training mode gradually solidifies, researchers propose a data-centric concept of artificial intelligence, emphasizing the development of higher-quality data to empower LLMs. Existing studies construct synthetic data for mathematical reasoning by expanding public datasets, thereby performing supervised fine-tuning of LLMs. However, these methods mostly focus on quantity while neglecting quality. The challenging samples fail to receive adequate consideration during data synthesis process, resulting in high construction costs, low-quality density, and serious data homogenization. This paper proposes a multi-agent environment called Virtual ClassRoom (VCR), which leverages various agents driven by LLM to construct high-quality diversified synthetic data. Inspired by the "Cone of Experience" educational theory, VCR introduces three experience levels (direct, iconic, and symbolic) into data synthesis process by analogy with human learning. A user-friendly instruction set and role-playing system are carefully designed, enabling VCR to autonomously plan the scale of synthetic data. This system covers various educational scenarios, including lecture, discussion, problem design and problem-solving. The Adaboost idea embodied in the global iterative process further promotes steady performance improvement. Extensive experiments show that the synthetic data generated by VCR possess higher quality density and generalization capability, which can give LLMs superior mathematical reasoning performance with the same scale.