arXiv research

Proposes a conservative exploration method for RL agents.

StepMix algorithm ensures safe exploration in reinforcement learning with near-optimal performance.

New algorithms ensure policies perform at least as good as a baseline in reinforcement learning.

The paper tackles safe exploration in RL by a conservative safety critic.

Proposes a method to avoid excessive exploration in reinforcement learning.

A new algorithm balances exploration and exploitation in online decision-making.

A challenging problem in complex networks is the network reconstruction problem from data. This work deals with a class of networks denoted as conserved networks, in which a flow associated with every edge and the flows are conserved at all non-source and non-sink nodes. We propose a novel polynomial time algorithm to …

Paper proposes an RL algorithm to ensure policy performance guarantees.

Data symmetries in neural networks can generate conserved quantities.

The paper explores symmetries and conserved charges on pre-symplectic manifolds.

We begin an exploration of parametric Backlund transformations for hyperbolic Monge-Ampere systems. We compute invariants for such transformations and explore the behavior of four examples regarding their invariants, symmetries, and conservation laws. We prove some preliminary results and indicate directions for furthe…

The problem of multi-armed bandits (MAB) asks to make sequential decisions while balancing between exploitation and exploration, and have been successfully applied to a wide range of practical scenarios. Various algorithms have been designed to achieve a high reward in a long term. However, its short-term performance m…

Safe exploration method for RL under disturbance ensures safety with probabilistic guarantees.

New algorithm improves online learning under performance constraints.

VaR-CPO optimizes VaR-constrained RL problems with conservative policy updates.

We explore the geometry of the Nahm-Schmid equations, a version of Nahm's equations in split signature. Our discussion ties up different aspects of their integrable nature: dimensional reduction from the Yang--Mills anti-self-duality equations, explicit solutions, Lax-pair formulation, conservation laws and spectral cu…

Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local an…

Paper explores weak solutions' regularity in critical dimensions without conservation law.

New batch RL method avoids overly optimistic policies.

BRAID fine-tunes diffusion models to optimize reward models in offline scenarios.

We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity solutions linked to order book formation and recovery is explored. The main result…

The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.

Theoretical analysis confirms non-conservative algorithms can converge to optimal policies.

Adapts safe policies for exploration in high-risk settings.

Study finds conserved quantities for two types of curves on conformal sphere.

New method finds unseen states for RL, improving performance.

Survey on conservation laws for geometric PDEs.

The paper optimizes LLM inference systems through queueing theory.

The article discusses conservation laws for polyharmonic maps and their applications.

Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.

Auto-CEI improves LLM reasoning by balancing assertiveness and conservativeness.

I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such equations. This provides an auxiliary differential equation satisfied by the conservatio…

Non-trivial conservation law found for a specific system.

This work connects symmetries and conserved quantities in machine learning.

Real-world applications require RL algorithms to act safely. During learning process, it is likely that the agent executes sub-optimal actions that may lead to unsafe/poor states of the system. Exploration is particularly brittle in high-dimensional state/action space due to increased number of low-performing actions. …

Conservation law for weakly harmonic mappings in high dimensions.

The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives …

Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitable submanifolds are constant under time evolution, the Kelvin circulation theorem being a well-known special case. More generally, conserved…

We study higher-order conservation laws of the non-linearizable elliptic Poisson equation $\frac{{\partial}^2 u}{\partial z \partial \bar{z}} = -f(u)$ as elements of the characteristic cohomology of the associated exterior differential system. The theory of characteristic cohomology determines a normal form for diffe…

New conservation laws found for polyharmonic maps in critical dimension.

MC-LSTM extends LSTM to conserve mass in neural networks.

The paper studies symmetries and conservation laws of non-diagonalisable hydrodynamic systems.

We present a connection between the Killing fields that arise in the loop-group approach to integrable systems and conservation laws viewed as elements of the characteristic cohomology. We use the connection to generate the complete set of conservation laws (as elements of the characteristic cohomology) for the Tzitzei…

We obtain necessary and sufficient conditions for the existence of "conservation laws" on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds. Examples of null hypersurfaces exhibiting such conservation laws include the standard null cones of Minkowski spacetime and the degenerate …

New neural network enforces mass conservation for better ice flow predictions.

The study finds resonance points in polarised curves with polynomial conserved quantities.

Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and extrinsic biharmonic maps. With the help of this conservation law we prove the continuit…

There is a well-known example of integrable conservative system on $S^2$, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on $S^2$ possessing an integral of fourth degree in moment…