The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations of the Riemann surface and the gravitino. Furthermore the action functional of no…
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48 results for “action functionals”
An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the di…
We consider the reduced Allen-Cahn action functional, which appears as the sharp interface limit of the Allen-Cahn action functional and can be understood as a formal action functional for a stochastically perturbed mean curvature flow. For suitable evolutions of generalized hypersurfaces this functional consists of th…
Study slice-regular polynomial functions via twistor space group actions.
problem Characterize slice-regular functions and their polynomial subclasses.
method Employ the twistor construction and group actions of .
result Characterize slice-regular functions with planar twistor lifts and normal classes of polynomials.
Morse inequalities for noncompact manifolds with group action.
problem Establishing inequalities for noncompact manifolds with group action.
method Using -Betti numbers and functions describing critical points.
result Morse inequalities given in terms of -Betti numbers and group functions.
A new RL paradigm reduces state-action-value function approximation inefficiency.
problem Challenges in state-action-value function approximation for RL.
method State Action Separable Reinforcement Learning (sasRL) decouples action space from value function learning.
result sasRL achieves up to 75% better performance than state-of-the-art MDP-based RL algorithms.
Motivated from the action functional for bosonic strings with extrinsic curvature term we introduce an action functional for maps between Riemannian manifolds that interpolates between the actions for harmonic and biharmonic maps. Critical points of this functional will be called interpolating sesqui-harmonic maps. In …
We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a funct…
The study proves curvature bounds for quotient spaces of isometric actions.
problem Proving curvature bounds for quotient spaces of isometric actions.
method Disintegrate absolutely continuous measures and define a functional to prove curvature bounds.
result Necessary and sufficient conditions for Ricci curvature to be bounded below.
We outline a cohomological treatment for multivalued (classical) action functionals. We point out that an application of Takens' theorem, after Zuckerman, Deligne and Freed, allows to conclude that multivalued functionals yield globally defined variational equations.
We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological spaces that admit functions similar to the Kempf-Ness function. The point of this…
New RL method handles large state-action spaces with complex models.
problem Complex models and large state-action spaces in reinforcement learning.
method π-KRVI, an optimistic modification of least-squares value iteration using kernel ridge regression.
result First order-optimal regret guarantees under general settings, improving over state of the art.
PQR estimates reward functions from actions and states without assuming state-only rewards.
problem Estimating reward functions from actions and states without state-only assumptions.
method Deep learning approach that sequentially estimates policy, Q-function, and reward.
result PQR uniquely recovers true reward with known transitions and bounds error with unknown transitions.
Smooth approximations for continuous functions on orbit spaces.
problem Approximating continuous functions on orbit spaces.
method Study of subcartesian spaces and proper Lie group actions.
result Continuous functions can be approximated by smooth functions.
We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as `stability functions'. We introduce a new stability invariant - the critical value of the coupling constant - defined as the minimal coupling constant for which the partition function converges.…
The paper studies critical points and flows of a -Hilbert functional on manifolds with circle actions.
problem Critical points and flows of the -Hilbert functional on manifolds with -actions.
method Analysis of -invariant -structures, reduction to a 6-dimensional quotient, and derivation of a negative -gradient flow.
result The unnormalized flow admits only trivial stationary configurations: flat connection, scalar-flat base metric, and constant fiber length.
Paper learns meaningful state and action representations from MDP trajectories.
problem Learning good state and action representations from MDP trajectories.
method Tensor decomposition, kernelization, importance sampling, low-Tucker-rank approximation.
result The learned state/action abstractions provide accurate approximations to latent block structures.
Study Hamiltonian diffeomorphisms on symplectic manifolds and properties of invariant convex functions.
problem Properties of invariant convex functions under Hamiltonian diffeomorphisms.
method Analysis of the adjoint action and properties of invariant convex functions.
result Continuous convex functions invariant under Hamiltonian diffeomorphisms are also invariant under strict rearrangements.
We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the Bloch-Wigner functions. We prove the first and second variation formulas for the cla…
The study classifies and investigates translators invariant under hyperpolar actions on symmetric spaces.
problem Understanding translators invariant under hyperpolar actions on symmetric spaces.
method Classification and investigation of translators given by functions invariant under hyperpolar actions.
result Classification and investigation of translators in symmetric spaces under hyperpolar actions.
Solves symplectic and conformal symplectic group actions equivalence problem.
problem Equivalence problem for symplectic and conformal symplectic group actions.
method Computing differential invariants via the Lie-Tresse theorem.
result Solves equivalence problem for symplectic and conformal symplectic group actions.
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.
Study of spectral invariants on CR contact manifolds with circle action.
problem Analytic torsion and eta-like invariants on CR contact manifolds.
method Interpret spectral series topologically and dynamically using Reeb flow.
result Spectral series can be interpreted both topologically and dynamically.
New algorithm for context bandits with continuous actions.
problem Efficient decision-making with unknown action structures.
method Reduction-style algorithm combining supervised learning.
result Proven to work in general and validated with experiments.
This paper presents the theory of non-smooth Lie group actions on chains of Banach manifolds. The rigorous functional analytic spaces are given to deal with quotients of such actions. A hydrodynamical example is studied in detail.
Paper optimizes Bayesian optimization for complex functions with macro-actions.
problem Optimizing complex, highly uncertain functions efficiently.
method Generalized GP upper confidence bound with macro-actions for scalable lookahead.
result Asymptotically optimal anytime variant of epsilon-Macro-GPO policy.
We consider stochastic multi-armed bandit problems with complex actions over a set of basic arms, where the decision maker plays a complex action rather than a basic arm in each round. The reward of the complex action is some function of the basic arms' rewards, and the feedback observed may not necessarily be the rewa…
ZOSPI improves RL policies with global value function exploitation.
problem Limited sample efficiency of PG algorithms in RL.
method Zeroth-order supervised policy improvement, leveraging global value function estimation.
result ZOSPI achieves competitive results with remarkable sample efficiency.
Network slicing promises to provision diversified services with distinct requirements in one infrastructure. Deep reinforcement learning (e.g., deep -learning, DQL) is assumed to be an appropriate algorithm to solve the demand-aware inter-slice resource management issue in network slicing by regarding the …
Deep RBVFs improve continuous control in RL.
problem Challenges in finding optimal actions for continuous actions in RL.
method Introduced deep radial-basis value functions (RBVFs) for continuous control.
result RBF-DQN significantly outperforms value-function-only baselines and is competitive with actor-critic algorithms.
A framework for reinforcement learning tackles CVRP with competitive results.
problem Optimizing routes for vehicles with limited capacity.
method Formulates action selection as a mixed-integer optimization problem, uses policy iteration to improve policies.
result Achieves an average gap of 1.7% with state-of-the-art OR methods on CVRP instances.
This paper optimizes slate decision systems for large action spaces.
problem Optimizing large-scale decision systems with arbitrary reward functions.
method A policy optimization framework with a novel relaxation of decision functions.
result Demonstrates the effectiveness of the proposed method on large action spaces.
Study lenient regret and good-action identification in Gaussian process bandits.
problem Optimizing function values above a certain threshold in Gaussian process bandits.
method Study lenient regret notions and introduce algorithms for finding good actions.
result Upper and lower bounds on lenient regret for GP-UCB and elimination algorithms.
We consider the problem of learning the optimal action-value function in the discounted-reward Markov decision processes (MDPs). We prove a new PAC bound on the sample-complexity of model-based value iteration algorithm in the presence of the generative model, which indicates that for an MDP with N state-action pairs a…
This is the second of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co--chains of a Frobenius algebra. We also prove that a there is dg--PROP action of a version of Sullivan Chord diagrams which acts on the…
Efficiently plans large MDPs with weak function approximations.
problem Planning in large MDPs with limited function approximation capabilities.
method Uses linear value function approximation with weak requirements and a generative oracle.
result Produces almost-optimal actions for any state with polynomial computation time.
Novel framework proves fast RL convergence in continuous spaces.
problem Analyzing stability in continuous state-action RL.
method Introduces a novel framework to analyze stability properties of RL.
result Highlights two key stability properties and demonstrates their satisfaction in RL.
Let be a compact connected strongly pseudoconvex CR manifold of dimension with a transversal CR action on . We establish an asymptotic expansion for the -th Fourier component of the Szegő kernel function as , where the expansion involves a contribution in terms of a d…
New RL method reduces sample complexity for large state-action spaces.
problem Handling large state-action spaces in RL with general Q-functions.
method Nonparametric Q-learning using kernel ridge regression.
result Sample complexity is order optimal with respect to ε and kernel complexity.
We study online reinforcement learning for finite-horizon deterministic control systems with {\it arbitrary} state and action spaces. Suppose that the transition dynamics and reward function is unknown, but the state and action space is endowed with a metric that characterizes the proximity between different states and…
A new RL algorithm POWR learns world models to estimate action-values.
problem Inaccessibility of explicit action-value functions in RL.
method Learning a world model using conditional mean embeddings and deriving action-value function via matrix operations.
result POWR algorithm converges to global optimum with proven rates.
Guillemin trace formula adapted for group actions.
problem Distributional trace for proper, cocompact group actions.
method Developing an equivariant version of the distributional trace.
result Equivariant Guillemin trace formula for group actions.
Efficient algorithms for planning in cooperative multi-agent reinforcement learning with combinatorial action spaces.
problem Planning in cooperative multi-agent reinforcement learning with a combinatorial action space.
method Efficient algorithms using local access to a simulator and linear function approximation, with improvements for additive feature decomposition and kernelized settings.
result Polynomial compute and query complexity in relevant problem parameters.
We construct a function of the edge-lengths of a triangulated surface whose variation under a rescaling of all the edges that meet at a vertex is the defect angle at that vertex. We interpret this function as a gravitational effective action on the triangulation, and the variation as a trace anomaly.
Kähler soliton surfaces are typically toric under generic conditions.
problem Understanding the symmetry of Kähler gradient Ricci solitons.
method Analyzing the integrability of the Hamiltonian system and the toric action.
result Kähler soliton surfaces are generically toric under certain conditions.
New RL approach uses future state and action visitation measures for better exploration.
problem Improving exploration in reinforcement learning.
method Intrinsic reward based on future state and action visitation measures, using contraction operators.
result Policies achieve good state-action space coverage and high performance.
We study here the action of subgroups of PSL(2,R) on the space of harmonic functions on the unit disc bounded by a common constant, as well as the relationship this action has with the foliated Liouville problem: Given a foliation of a compact manifold by Riemannian leaves and a leafwise harmonic continuous function on…
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short intro…