Categorical semantics of compositional reinforcement learning

• URL: http://arxiv.org/abs/2208.13687v1
• Date: Mon, 29 Aug 2022 15:51:36 GMT
• Title: Categorical semantics of compositional reinforcement learning
• Authors: Georgios Bakirtzis, Michail Savvas, Ufuk Topcu
• Abstract summary: Reinforcement learning (RL) often requires decomposing a problem into subtasks and composing learned behaviors on these tasks. We develop a framework for a emphcompositional theory of RL using a categorical point of view. We show that $mathsfMDP$ admits natural compositional operations, such as certain fiber products and pushouts.
• Score: 25.752647944862183
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reinforcement learning (RL) often requires decomposing a problem into subtasks and composing learned behaviors on these tasks. Compositionality in RL has the potential to create modular subtask units that interface with other system capabilities. However, generating compositional models requires the characterization of minimal assumptions for the robustness of the compositional feature. We develop a framework for a \emph{compositional theory} of RL using a categorical point of view. Given the categorical representation of compositionality, we investigate sufficient conditions under which learning-by-parts results in the same optimal policy as learning on the whole. In particular, our approach introduces a category $\mathsf{MDP}$, whose objects are Markov decision processes (MDPs) acting as models of tasks. We show that $\mathsf{MDP}$ admits natural compositional operations, such as certain fiber products and pushouts. These operations make explicit compositional phenomena in RL and unify existing constructions, such as puncturing hazardous states in composite MDPs and incorporating state-action symmetry. We also model sequential task completion by introducing the language of zig-zag diagrams that is an immediate application of the pushout operation in $\mathsf{MDP}$.

Related papers

• Interpreting token compositionality in LLMs: A robustness analysis [10.777646083061395]
  Constituent-Aware Pooling (CAP) is a methodology designed to analyse how large language models process linguistic structures. CAP intervenes in model activations through constituent-based pooling at various model levels. Our findings highlight fundamental limitations in current transformer architectures regarding compositional semantics processing and model interpretability.
  arXiv  Detail & Related papers  (2024-10-16T18:10:50Z)
• Do Large Language Models Have Compositional Ability? An Investigation into Limitations and Scalability [12.349247962800813]
  Large language models (LLMs) have emerged as powerful tools for many AI problems. They exhibit remarkable in-context learning (ICL) capabilities. How they approach composite tasks remains an open and largely underexplored question.
  arXiv  Detail & Related papers  (2024-07-22T15:22:34Z)
• What makes Models Compositional? A Theoretical View: With Supplement [60.284698521569936]
  We propose a general neuro-symbolic definition of compositional functions and their compositional complexity. We show how various existing general and special purpose sequence processing models fit this definition and use it to analyze their compositional complexity.
  arXiv  Detail & Related papers  (2024-05-02T20:10:27Z)
• Discovering Abstract Symbolic Relations by Learning Unitary Group Representations [7.303827428956944]
  We investigate a principled approach for symbolic operation completion (SOC) SOC poses a unique challenge in modeling abstract relationships between discrete symbols. We demonstrate that SOC can be efficiently solved by a minimal model - a bilinear map - with a novel factorized architecture.
  arXiv  Detail & Related papers  (2024-02-26T20:18:43Z)
• SymbolicAI: A framework for logic-based approaches combining generative models and solvers [9.841285581456722]
  We introduce SymbolicAI, a versatile and modular framework employing a logic-based approach to concept learning and flow management in generative processes. We treat large language models (LLMs) as semantic solvers that execute tasks based on both natural and formal language instructions.
  arXiv  Detail & Related papers  (2024-02-01T18:50:50Z)
• Building Minimal and Reusable Causal State Abstractions for Reinforcement Learning [63.58935783293342]
  Causal Bisimulation Modeling (CBM) is a method that learns the causal relationships in the dynamics and reward functions for each task to derive a minimal, task-specific abstraction. CBM's learned implicit dynamics models identify the underlying causal relationships and state abstractions more accurately than explicit ones.
  arXiv  Detail & Related papers  (2024-01-23T05:43:15Z)
• Discrete, compositional, and symbolic representations through attractor dynamics [51.20712945239422]
  We introduce a novel neural systems model that integrates attractor dynamics with symbolic representations to model cognitive processes akin to the probabilistic language of thought (PLoT) Our model segments the continuous representational space into discrete basins, with attractor states corresponding to symbolic sequences, that reflect the semanticity and compositionality characteristic of symbolic systems through unsupervised learning, rather than relying on pre-defined primitives. This approach establishes a unified framework that integrates both symbolic and sub-symbolic processing through neural dynamics, a neuroplausible substrate with proven expressivity in AI, offering a more comprehensive model that mirrors the complex duality of cognitive operations
  arXiv  Detail & Related papers  (2023-10-03T05:40:56Z)
• Dynamic MOdularized Reasoning for Compositional Structured Explanation Generation [29.16040150962427]
  We propose a dynamic modularized reasoning model, MORSE, to improve compositional generalization of neural models. MORSE factorizes the inference process into a combination of modules, where each module represents a functional unit. We conduct experiments for increasing lengths and shapes of reasoning trees on two benchmarks to test MORSE's compositional generalization abilities.
  arXiv  Detail & Related papers  (2023-09-14T11:40:30Z)
• On Conditional and Compositional Language Model Differentiable Prompting [75.76546041094436]
  Prompts have been shown to be an effective method to adapt a frozen Pretrained Language Model (PLM) to perform well on downstream tasks. We propose a new model, Prompt Production System (PRopS), which learns to transform task instructions or input metadata, into continuous prompts.
  arXiv  Detail & Related papers  (2023-07-04T02:47:42Z)
• A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning [132.45959478064736]
  We propose a general framework that unifies model-based and model-free reinforcement learning. We propose a novel estimation function with decomposable structural properties for optimization-based exploration. Under our framework, a new sample-efficient algorithm namely OPtimization-based ExploRation with Approximation (OPERA) is proposed.
  arXiv  Detail & Related papers  (2022-09-30T17:59:16Z)
• Semantic Representation and Dependency Learning for Multi-Label Image Recognition [76.52120002993728]
  We propose a novel and effective semantic representation and dependency learning (SRDL) framework to learn category-specific semantic representation for each category. Specifically, we design a category-specific attentional regions (CAR) module to generate channel/spatial-wise attention matrices to guide model. We also design an object erasing (OE) module to implicitly learn semantic dependency among categories by erasing semantic-aware regions.
  arXiv  Detail & Related papers  (2022-04-08T00:55:15Z)
• Compositionality as Lexical Symmetry [42.37422271002712]
  In tasks like semantic parsing, instruction following, and question answering, standard deep networks fail to generalize compositionally from small datasets. We present a domain-general and model-agnostic formulation of compositionality as a constraint on symmetries of data distributions rather than models. We describe a procedure called LEXSYM that discovers these transformations automatically, then applies them to training data for ordinary neural sequence models.
  arXiv  Detail & Related papers  (2022-01-30T21:44:46Z)
• How Fine-Tuning Allows for Effective Meta-Learning [50.17896588738377]
  We present a theoretical framework for analyzing representations derived from a MAML-like algorithm. We provide risk bounds on the best predictor found by fine-tuning via gradient descent, demonstrating that the algorithm can provably leverage the shared structure. This separation result underscores the benefit of fine-tuning-based methods, such as MAML, over methods with "frozen representation" objectives in few-shot learning.
  arXiv  Detail & Related papers  (2021-05-05T17:56:00Z)
• Model-Invariant State Abstractions for Model-Based Reinforcement Learning [54.616645151708994]
  We introduce a new type of state abstraction called textitmodel-invariance. This allows for generalization to novel combinations of unseen values of state variables. We prove that an optimal policy can be learned over this model-invariance state abstraction.
  arXiv  Detail & Related papers  (2021-02-19T10:37:54Z)
• Learning Robust State Abstractions for Hidden-Parameter Block MDPs [55.31018404591743]
  We leverage ideas of common structure from the HiP-MDP setting to enable robust state abstractions inspired by Block MDPs. We derive instantiations of this new framework for both multi-task reinforcement learning (MTRL) and meta-reinforcement learning (Meta-RL) settings.
  arXiv  Detail & Related papers  (2020-07-14T17:25:27Z)
• FLAMBE: Structural Complexity and Representation Learning of Low Rank MDPs [53.710405006523274]
  This work focuses on the representation learning question: how can we learn such features? Under the assumption that the underlying (unknown) dynamics correspond to a low rank transition matrix, we show how the representation learning question is related to a particular non-linear matrix decomposition problem. We develop FLAMBE, which engages in exploration and representation learning for provably efficient RL in low rank transition models.
  arXiv  Detail & Related papers  (2020-06-18T19:11:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.