arXiv research

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

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

An online reinforcement learning algorithm is anytime if it does not need to know in advance the horizon T of the experiment. A well-known technique to obtain an anytime algorithm from any non-anytime algorithm is the "Doubling Trick". In the context of adversarial or stochastic multi-armed bandits, the performance of …

BCPO optimizes offline RL policies by converting uncertainty into conservative bounds.

HAMBO estimates policy performance by hallucinating worst-case trajectories, providing valid lower bounds.

The paper extends a learning heuristic to high-dimensional contexts, reducing the risk of unusual actions.

Canary optimizes VaR-constrained RL problems with a conservative bound using Cantelli's inequality.

Proposes a conservative exploration method for RL agents.

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…

This work connects symmetries and conserved quantities in machine learning.

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

Unified neural network framework for context-aware Gaussian overbounds in uncertainty propagation.

CQL learns conservative Q-functions to improve offline RL performance.

RORL improves offline RL robustness with conservative smoothing.

Paper proposes an RL algorithm to ensure policy performance guarantees.

A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.

While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will eventually learn a good or optimal policy, there is no guarantee on the quality of the in…

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

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…

Two new algorithms optimize rewards while respecting safety constraints in sequential decisions.

Sharp bounds on heat kernel derivatives on incomplete manifolds.

New rigorous uncertainty bounds for Gaussian Process regression.

In many fields such as digital marketing, healthcare, finance, and robotics, it is common to have a well-tested and reliable baseline policy running in production (e.g., a recommender system). Nonetheless, the baseline policy is often suboptimal. In this case, it is desirable to deploy online learning algorithms (e.g.,…

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

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

The study extends conserved quantities theory to non-compact boundary initial data sets.

The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the…

Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e., guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in cont…

Survey on conservation laws for geometric PDEs.

We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for harmonic maps into homogeneous s…

New algorithm reduces pricing error by a factor of T^2/3.

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

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…

COME replaces entropy minimization to prevent model collapse.

Non-trivial conservation law found for a specific system.

Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative volatility enable us to super-hedge convex and concave payoffs respectively. The ide…

Geometric technique determines exactness of SDP robustness certificate.

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…

New conservation laws found for polyharmonic maps in critical dimension.

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 …

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

In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past the common approach has been to use various "group sparsity-inducing" norms such as the Group LASSO norm for this purpose. By using the theory of convex relaxations, we show that it is also po…

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.