Characterizes continuity of monotone functionals in mixed topology.
problem Continuity of monotone functionals in mixed topology.
method Characterization through lower semicontinuity and dual representations.
result Continuity in mixed topology is equivalent to dual representation in terms of countably additive measures.
Regulated curves on Banach manifolds with continuous projections and regulated derivatives are studied.
problem Regulated curves on Banach manifolds with continuous projections and regulated derivatives.
method Building a Banach manifold structure on the set of such curves.
result Existence of a 'local addition' on such a manifold for any Banach manifold.
Introduces strong equilibrium for time-inconsistent stopping problems in continuous time.
problem Time-inconsistent stopping problems in continuous time.
method Introduces strong equilibrium, compares with existing mild and weak equilibria, and provides an iteration method to construct optimal mild equilibria.
result Optimal mild equilibria are always strong equilibria under certain conditions.
HyBO optimizes hybrid structures using diffusion kernels.
problem Optimizing complex interactions between discrete and continuous variables.
method HyBO uses diffusion kernels over hybrid spaces with additive kernel formulation.
result HyBO significantly outperforms state-of-the-art methods on real-world benchmarks.
Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strate…
CPR adds entropy maximization to improve continual learning methods.
problem Catastrophic forgetting in continual learning.
method Classifier-Projection Regularization (CPR) adds an entropy maximization term to existing regularization methods.
result CPR improves accuracy and plasticity in continual learning methods.
UCL uses uncertainty to improve continual learning without extra memory.
problem Memory and performance issues in continual learning.
method Adapts Bayesian online learning with variational inference, introducing node-wise uncertainty and stability terms.
result UCL outperforms state-of-the-art methods on supervised and reinforcement learning tasks.
New method tackles catastrophic forgetting and order-sensitivity in continual learning.
problem Catastrophic forgetting and order-sensitivity in continual learning.
method Additive Parameter Decomposition (APD) to represent task parameters as a sum of shared and adaptive parts.
result Significantly outperforms state-of-the-art methods in accuracy, scalability, and order-robustness.
CAM-GAN improves GANs for continual learning with efficient feature map transformations.
problem Efficient continual learning for GANs with reduced parameter growth.
method Designing and leveraging parameter-efficient feature map transformations, including global and task-specific parameters, residual bias, and Fisher information matrix.
result Significantly improved model performance and high-quality samples with fewer parameters.
Framework for robust RL in continuous control with model misspecification.
problem Model misspecification in reinforcement learning for continuous control.
method Integrates robustness into MPO algorithm through worst-case expected return objective and entropy regularization.
result Robust and soft-robust policies outperform non-robust policies in various domains.
We study the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we show that the renormalized volume is continuous under the appropriate notion of limit. This result generalizes previous work in the subject…
The paper tackles contextual bandits with continuous actions using smoothing and zooming techniques.
problem Learning with continuous action spaces in the context of contextual bandits.
method The approach involves smoothing and zooming techniques to handle the continuous action space and unknown smoothness parameters.
result Improved regret bounds and adaptive algorithms for contextual bandits with continuous actions.
For a large class of vanilla contingent claims, we establish an explicit Föllmer-Schweizer decomposition when the underlying is an exponential of an additive process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to models derived from the electricity market a…
Improved density estimation for mixed discrete-continuous data.
problem Inconsistent density estimation for mixtures of continuous and discrete data.
method Modification of existing nonparametric density estimation methods to handle mixed discrete-continuous data.
result Improved consistency and empirical performance for mixed discrete-continuous data.
New method prevents forgetting in LLMs by dynamically identifying task-specific subspaces.
problem Catastrophic forgetting in continual learning of LLMs.
method Adaptive Singular Value Decomposition (SVD) for constrained full fine-tuning.
result Achieves state-of-the-art results in continual learning benchmarks.
JME continually estimates data moments privately and accurately.
problem Private and accurate continual estimation of data moments.
method Uses matrix mechanism and joint sensitivity analysis.
result Improves accuracy in estimating mean and covariance with reduced noise.
Unique continuation property for measures in high dimensions.
problem Understanding the structure of measures in high-dimensional spaces.
method Analyzing locally uniformly distributed measures and their supports.
result Locally uniformly distributed measures satisfy a unique continuation property.
New theorem for deep neural networks improves classification margins.
problem Improving classification margins in deep neural networks.
method Local class-purity theorem and margin p-values for training and testing samples.
result Enhanced understanding and computation of classification margins.
Study on volume continuity of Lagrangian submanifolds.
problem Lower semi-continuity of Lagrangian volume.
method Analysis of volume properties with respect to Hofer- and γ-distances.
result Volume is γ-lower semi-continuous in two specific cases.
Paper tackles overestimation bias in continuous control, improving performance by 25%.
problem Overestimation bias in off-policy learning.
method Truncated Quantile Critics (TQC) combines distributional representation, truncation, and ensembling of critics.
result TQC outperforms state-of-the-art methods by 25% on the Humanoid environment.
Framework for learning sparse DAGs from data.
problem Learning sparse directed acyclic graphs (DAGs) from data.
method Algebraic characterization of DAGs extended to nonparametric SEM, continuous optimization problem.
result General framework applicable to various nonparametric and semiparametric models.
Develops a framework for modeling set-valued data in continuous-time.
problem Handling sequences where each event is associated with a set of items.
method General framework for modeling set-valued data, developed inference methods, and importance sampling techniques.
result Orders-of-magnitude improvements in efficiency for probabilistic queries over direct sampling.
We solve continuous-time latent SDE identifiability using diffusion shifts.
problem Identifiability of latent SDEs in continuous-time time series.
method Environment-induced shifts in diffusion covariance for additive-noise latent SDEs.
result Two diagonal diffusion regimes with distinct variance ratios identify latent coordinates up to permutation and scaling.
A method to prevent VAE forgetting across tasks.
problem Catastrophic forgetting in VAEs when learning sequentially.
method Learn an end-to-end approximation of the aggregated posterior as a prior for each task, encouraging diversity among components.
result The method avoids catastrophic forgetting in various datasets.
Survey of continuous volatility models, focusing on fractional and rough methods.
problem Stylized facts driving continuous volatility modeling.
method Historical development and fractional/rough methods.
result Characterization of landmark models and recent advances.
Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.
problem Improving the convergence rate of stochastic gradient descent and gossip algorithms.
method Introducing a continuized variant of Nesterov acceleration, which mixes variables continuously and takes gradient steps at random times.
result The continuized Nesterov acceleration achieves convergence rates similar to Nesterov's original acceleration but with random parameters.
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive models. The proposed sparse difference of convex additive models (SDCAM) can est…
IRL addresses weaknesses in DDPG and A3C for continuous reinforcement learning.
problem Theoretical weaknesses in DDPG and A3C for continuous reinforcement learning.
method IRL based on stochastic differential equations, ensuring action continuity and variance control.
result IRL method guarantees action continuity and variance control, allowing positive interaction with the environment.
This note classifies splittable lattices in a specific Lie group.
problem Classifying splittable lattices in a metabelian solvable Lie group.
method Description and classification of splittable lattices in G:=RntimesηRm. result Classification of splittable lattices in the specified Lie group.
Training a neural network for a classification task typically assumes that the data to train are given from the beginning. However, in the real world, additional data accumulate gradually and the model requires additional training without accessing the old training data. This usually leads to the catastrophic forgettin…
Study utility maximization with delayed information in continuous time Gaussian markets.
problem Maximizing utility with delayed information in continuous time Gaussian markets.
method Purely probabilistic approach based on Radon-Nikodym derivatives of Gaussian measures.
result Solution for optimal control and value in a specific Gaussian framework.
The paper explores continuous inverse ambiguous functions on various Lie groups.
problem Existence of continuous inverse ambiguous functions on Lie groups.
method Investigation of continuous inverse ambiguous functions on specific Lie groups.
result Existence of continuous inverse ambiguous functions on various Lie groups.
Paper explores arbitrage and CAPM in continuous time.
problem Understanding arbitrage and CAPM in continuous time.
method Analyzes instantaneous arbitrage and its relation to CAPM.
result Arbitrage and CAPM arguments differ in assumptions about the market portfolio.
We price and hedge American options robustly in continuous time.
problem Pricing and hedging American options in continuous time with model uncertainty.
method Assumes continuous semimartingale asset prices and closed convex constraints on volatility. Proves robust pricing-hedging duality and identifies American options as European options on an enlarged space.
result We prove robust pricing-hedging duality and show it holds against richer models with dynamic trading of European options.
We extend the Weil-Petersson metric to a projective variety with continuous local potentials.
problem Continuity of the Weil-Petersson potential on moduli spaces of Kähler-Einstein manifolds and varieties.
method Proving the extension of the Weil-Petersson metric as a closed positive current with continuous local potentials.
result The Weil-Petersson metric extends uniquely to the projective variety as a closed positive current with continuous local potentials.
A new STAR framework models integer-valued data with flexible distributions.
problem Modeling integer-valued data with flexibility and accuracy.
method Simultaneously Transforming and Rounding (STAR) a continuous-valued process.
result STAR framework designs a new BART model for integer-valued data with impressive predictive accuracy.
We study a portfolio selection problem in a continuous-time Itô-Markov additive market with prices of financial assets described by Markov additive processes which combine Lévy processes and regime switching models. Thus the model takes into account two sources of risk: the jump diffusion risk and the regime switching …
Analyzes non-Markovian environments in stochastic approximation.
problem Understanding learning mechanisms in non-ergodic, non-Markovian settings.
method Analytic framework for transformer learning and continual learning.
result Proposes a new approach to transformer and continual learning.
In recent years, there is a growing interest in learning Bayesian networks with continuous variables. Learning the structure of such networks is a computationally expensive procedure, which limits most applications to parameter learning. This problem is even more acute when learning networks with hidden variables. We p…
Recall that Federer-Fleming defined the notion of flat convergence of submanifolds of Euclidean space to solve the Plateau problem. Here we prove the upper semicontinuity of Neumann eigenvalues of the submanifolds when they converge in the flat sense without losing volume. With an additional condition on the boundaries…
New method bounds causal effects in continuous distributions.
problem Estimating causal effects with general instrumental variables.
method Gradient-based optimization for computationally intractable bounds.
result Bounds capture causal effect when additive methods fail.
BART is extended to handle various response variables.
problem Modeling nonlinear regression functions for diverse response types.
method Generalized Bayesian Additive Regression Trees (GBART) for exponential family distributions.
result The posterior concentrates at a minimax rate for certain response distributions.
Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.
problem Optimizing control actions in unknown continuous-time systems over a finite time horizon.
method Least-squares algorithm based on continuous-time observations and controls, with perturbation analysis and parameter estimation error analysis.
result Logarithmic regret bound of order O((lnM)(lnlnM)). The paper proves Γ-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.
problem Proving convergence of discrete tangent-point energies to continuous energies and ropelength.
method Using biarc curves and interpolation, the paper proves Γ-convergence of discretized tangent-point energies to the continuous tangent-point energies and ropelength functional. result Discrete almost minimizing biarc curves converge to ropelength minimizers and minimizers of continuous tangent-point energies.
Investment strategy optimization from discrete to continuous models.
problem Optimizing investment strategies and stopping times in both continuous and discrete settings.
method Characterized value functions via quadratic reflected BSDEs for continuous case, discretized BSDEs for discrete case, and derived uniform convergence rates.
result Uniform convergence and rate from discrete to continuous quadratic reflected BSDEs.
CANDI solves the gap between continuous and discrete diffusion models for text generation.
problem Underperformance of continuous diffusion models in discrete data domains.
method Introduces token identifiability and a hybrid framework (CANDI) to decouple discrete and continuous corruption.
result CANDI successfully avoids temporal dissonance, enabling continuous diffusion benefits for discrete spaces.
In a continuous-time setting where a risk-averse agent controls the drift of an output process driven by a Brownian motion, optimal contracts are linear in the terminal output; this result is well-known in a setting with moral hazard and -under stronger assumptions - adverse selection. We show that this result continue…
Paper introduces CRLMaze, a new benchmark for continual reinforcement learning in 3D non-stationary environments.
problem Challenges of training reinforcement learning agents in high-dimensional, always-changing environments.
method End-to-end model-free continual reinforcement learning strategy.
result Competitive results in a complex 3D non-stationary task, outperforming four baselines.