In this paper we develop a general conceptual approach to the problem of existence of action-angle variables for dynamical systems, which establishes and uses the fundamental conservation property of associated torus actions: anything which is preserved by the system is also preserved by the associated torus actions. T…
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48 results for “action variables”
In this paper we analyze the obstructions to the existence of global action-angle variables for regular non-commutative integrable systems (NCI systems) on Poisson manifolds. In contrast with local action-angle variables, which exist as soon as the fibers of the momentum map of such an integrable system are compact, gl…
In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how to obtain the invariantized Euler-Lagrange equations and the space of conservati…
Phenomenological Causalitystat.ME
A new concept of causality for abstract phenomena.
problem Unclear definition of causality in real-life variables.
method Introduces 'phenomenological causality' based on elementary actions.
result Defines causal structure without hard-wired links.
Uplifting Banditsstat.ML
UCB algorithms estimate uplifts in multi-variable reward systems.
problem Marketing campaigns and recommender systems with multiple outcome variables.
method UCB-style algorithms for estimating uplifts over a baseline.
result Sublinear regret bounds for multiple problem variants.
To address the challenge of backpropagating the gradient through categorical variables, we propose the augment-REINFORCE-swap-merge (ARSM) gradient estimator that is unbiased and has low variance. ARSM first uses variable augmentation, REINFORCE, and Rao-Blackwellization to re-express the gradient as an expectation und…
Extends integrability to cosymplectic manifolds.
problem Integrability of Hamiltonian systems on cosymplectic manifolds.
method Extended Arnold-Liouville and noncommutative integrability to cosymplectic manifolds, proved a variant of non-commutative integrability for specific fields, constructed action-angle variables.
result Variant of non-commutative integrability for evaluation and Reeb vector fields on cosymplectic manifolds.
Paper tackles action selection in deep RL, proposing a data-driven approach.
problem High-dimensional action selection in deep RL environments.
method Data-driven approach with knockoff sampling for minimal sufficient actions.
result Method surpasses alternative techniques in performance and rewards.
Introduction to Latent Variable Energy-Based Models: A Path Towards Autonomous Machine Intelligencecs.LG
Future autonomous systems need reliable world models and complex action sequences.
problem Current automated systems lack reliable world models and complex action sequences.
method Introduce energy-based and latent variable models combined in a hierarchical joint embedding predictive architecture (H-JEPA).
result Combining energy-based and latent variable models in H-JEPA can lead to reliable world models and complex action sequences.
ARL and Hawkes processes improve market-making strategies with variable volatility.
problem Enhancing market-making strategies to adapt to varying volatility levels and self-exciting behaviors.
method Integrates ARL, Hawkes processes, and variable volatility levels; shifts from Poisson to Hawkes process.
result 4-action MM trained in low-volatility environment adapts to high-volatility conditions, providing stable performance.
Latent variable models improve RL by facilitating efficient learning and exploration.
problem Improving sample efficiency in reinforcement learning.
method Representation view of latent variable models for state-action value functions, incorporating kernel embeddings and UCB exploration.
result Established sample complexity of the proposed approach in online and offline settings, demonstrated superior performance in benchmarks.
Recourse explanations can become invalid if collective actions change statistical data.
problem Recourse explanations may become invalid due to collective behavior changing data statistics.
method Formal characterization of conditions under which recourse explanations remain valid under performativity.
result Recourse actions may become invalid if they are influenced by or intervene on non-causal variables.
A new algorithm uses IVs to learn optimal policies from observational data.
problem Learning optimal policies from unobserved variable confounded data.
method IV-aided Value Iteration (IVVI) algorithm based on conditional moment restrictions.
result First provably efficient algorithm for instrument-aided offline RL.
We introduce a notion of the noncommutative integrability within a framework of contact geometry.
A new method for disentangling action sequences improves model stability.
problem Challenges in unsupervised disentanglement learning due to incomplete theories and abstract notions.
method Introducing disentangling action sequences and a novel fractional variational autoencoder (FVAE) framework.
result FVAE improves the stability of disentanglement for action sequences.
Paper develops IV method for consistent OPE in confounded MDPs.
problem Confounding variables in observational data affect OPE effectiveness.
method Instrumental variable approach for consistent off-policy evaluation.
result IV method enables correct identification of target policy's value.
In this paper, the symmetry group of a differential system of n quadratic homogeneous first order ODEs of n variables is studied. For this purpose, we consider the action of both point and contact transformations to signify the corresponding Lie algebras. We also find the independent differential invariants of these ac…
The paper computes infinitesimals for group actions on a multispace of curves.
problem Examining group actions on a multispace of curves.
method Formal study using recursion relations, closely mimicking jet space prolongation.
result Produces a recursion relation for infinitesimals in the multispace.
The interplay between the Hamilton-Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.
We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the causality in the evolution of dependent stochastic variables. We demonstrate this pr…
Paper proposes a new HMM approach for better action recognition.
problem Capturing complex temporal dependency patterns in skeleton-based actions.
method Introduces a hierarchical HMM with a latent variable layer for dynamic inference.
result Proposed approach effectively models complex sequential data and handles missing values.
We show that, when considering the scaling factor as an affine variable, the coefficients of the asymptotic expansion of the spectral action on a (Euclidean) Robertson-Walker spacetime are periods of mixed Tate motives, involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces and div…
Developing a dialogue agent that is capable of making autonomous decisions and communicating by natural language is one of the long-term goals of machine learning research. Traditional approaches either rely on hand-crafting a small state-action set for applying reinforcement learning that is not scalable or constructi…
Proposes hybrid reinforcement learning for both discrete and continuous control problems.
problem Real-world control problems involving both discrete and continuous decision variables.
method Solves hybrid problems by optimizing for discrete and continuous actions simultaneously.
result Efficiently solves hybrid reinforcement learning problems and improves upon expert heuristics.
We study the classification problem of singularities of function-germs with harmonic leading terms of two variables under the right-equivalence. We study the classification in the cases that the order of function-germs is at most 7. Moreover, we observe that the multiple actions of Laplacian appear for the classificati…
A new, simplified form of 10D supergravity action is derived up to all fermion orders.
problem Deriving a simplified form of 10D supergravity action up to all fermion orders.
method Generalised geometry and second-order formalism to upgrade calculations to all orders in fermions.
result A strikingly simple form of the action and supersymmetry transformations are obtained.
Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability distribution for the interventional distribution resulting from the action. In many case…
The paper classifies symplectic invariants of specific singularities in integrable Hamiltonian systems.
problem Classifying symplectic invariants of singularities in integrable Hamiltonian systems.
method Smooth symplectic classification of Lagrangian fibrations near singularities.
result Action variables form complete symplectic invariants for parabolic orbits and cuspidal tori.
A new framework for structured bandits using influence diagrams and variational Thompson sampling.
problem Complex statistical dependencies in structured bandit problems.
method Influence diagram framework, variational Thompson sampling, tracking structured posterior distribution.
result Empirically evaluated algorithms perform as well as or better than existing baselines.
Intelligent agents can learn to represent the action spaces of other agents simply by observing them act. Such representations help agents quickly learn to predict the effects of their own actions on the environment and to plan complex action sequences. In this work, we address the problem of learning an agent's action…
Causal Bayesian networks interpret actions as interventions to connect models to real-world outcomes.
problem Connecting causal model predictions to real-world outcomes.
method Formal framework to interpret actions as interventions and prove impossibility results.
result No non-circular interpretation exists that satisfies natural desiderata without violating some.
New model predicts drug effects across various cell types using causal imputation.
problem Predict drug effects across different cell types given limited data.
method Introduces a novel SCM-based model class with latent factor structure and uses Synthetic Interventions estimator.
result Method outperforms other matrix completion approaches in drug repurposing dataset.
New algorithm identifies best intervention without graph knowledge.
problem Finding best intervention in causal bandit setting with unknown graph.
method Additive combinatorial linear bandit problem with action-elimination algorithm.
result One can identify best intervention without explicitly learning graph parents.
Special homogeneous curvesmath.DG
Classifies special homogeneous curves with polynomial equations.
problem Identifying and classifying special homogeneous curves.
method Analyzing homogeneous polynomials and their level sets with group actions.
result All special homogeneous curves are classified.
Paper develops a method to estimate value of a policy in confounded MDPs.
problem Estimating value of a policy in the presence of unmeasured confounders.
method Uses auxiliary variables to identify target policy's value in a confounded MDP.
result Develops an off-policy value estimator robust to model misspecification.
Optimizes predictions for specific tasks using parametrized decision analysis.
problem Optimizing predictions for specific decision tasks of interest.
method Designs a class of parametrized actions for Bayesian decision analysis.
result Derives efficient and interpretable solutions for various action parametrizations and loss functions.
We study the classification problem of singularities of function-germs with harmonic leading terms of two variables under the right-equivalence. We observe that the multiple actions of Laplacian appear for the classifications of such class of function-germs.
Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced directly from the residue theorem of Jeffrey and Kirwan. A characterization of the ke…
We propose to meta-learn causal structures based on how fast a learner adapts to new distributions arising from sparse distributional changes, e.g. due to interventions, actions of agents and other sources of non-stationarities. We show that under this assumption, the correct causal structural choices lead to faster ad…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we explicitly determine the dependance of coefficients of generalized symmetries fro…
Study tackles OPE in confounded settings, estimating policy value from proxies.
problem Difficulty in OPE due to unobserved confounders in infinite-horizon RL.
method Two-stage approach: estimating stationary distribution ratios and combining optimal balancing.
result Policy value can be identified from off-policy data with proxies and latent variable model.
Fast covariance calculation is required both for SLAM (e.g.~in order to solve data association) and for evaluating the information-theoretic term for different candidate actions in belief space planning (BSP). In this paper we make two primary contributions. First, we develop a novel general-purpose incremental covaria…
Introduces group-valued momentum maps for symplectic fiber bundles.
problem Determining momentum maps for non-classical actions of automorphism groups.
method Develops a general framework for group-valued momentum maps.
result Illustrates the power of group-valued momentum maps with various examples.
New framework for AI to learn causal models through experience.
problem Lack of guidance for variable choice and interventions in causal models for AI.
method Defines actions as state space transformations, introduces causal variables, and identifies interventions.
result Clarifies the concept of interventions and makes causal representation learning clearer.
Special homogeneous surfacesmath.DG
Classifies special homogeneous surfaces with unique properties.
problem Classifying hyperbolic polynomials with specific actions.
method Analyzes hyperbolic level sets and restricts negative Hessians.
result Existence of a finite number of special homogeneous surfaces with unique curvature.
Study of algebraic links in lens spaces, proving they are fibered and finding examples.
problem Understanding algebraic links in lens spaces.
method Investigation of polynomials invariant under a -action on the 3-sphere, studying links and their properties.
result All algebraic links in lens spaces are fibered, with results on Seifert genus.
Stochastic Q-learning tackles large action spaces with reduced computation.
problem Effective decision-making in complex environments with large discrete action spaces.
method Stochastic value-based RL approaches that consider a sublinear number of actions in each iteration.
result Stochastic Q-learning achieves near-optimal returns with significantly reduced computation time.
New method improves weakly-supervised action localization.
problem Locating action segments in videos with limited labels.
method Explicitly models key instance assignment as hidden variable using EM framework.
result Achieves state-of-the-art performance on THUMOS14 and ActivityNet1.2 benchmarks.