This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.
problem Pathwise gradient estimators in variational inference have high variance, leading to inefficient optimization.
method Apply zero-variance control variates to pathwise gradient estimators.
result Zero-variance control variates can significantly reduce the variance of pathwise gradient estimators without requiring complex assumptions.
We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterizati…
We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the transport equation to construct adaptive control variates that can be used to construct…
NM-PPG optimizes adaptive feature acquisition in POMDPs for better predictions.
problem Optimizing adaptive feature acquisition in prediction problems with costly features.
method Non-myopic pathwise policy gradients (NM-PPG) with continuous relaxation and straight-through rollout.
result NM-PPG outperforms state-of-the-art AFA methods on synthetic and real-world datasets.
A scalable method for BED with implicit models using approximate gradients.
problem Efficiently estimating posterior distribution and maximizing MI for implicit models.
method Stochastic approximate gradient ascent with smoothed variational MI estimator.
result Significantly improves scalability of BED in high-dimensional problems.
A new method in finance without probabilities or integrals.
problem Creating a model-free approach to continuous-time finance.
method Pathwise approach using causal functional calculus and transition principle of Isaacs.
result A fully non-linear path-dependent equation characterizes optimal solutions.
The paper speeds up hyperparameter optimisation in Gaussian processes.
problem Scaling hyperparameter optimisation to large datasets.
method Improvements to linear system solvers (pathwise gradient, warm starting, early stopping).
result Speed-ups of up to 72x and residual norm decreases of up to 7x.
The paper optimizes bridge-type estimators for sparse models using pathwise methods.
problem Sparse parametric models with adaptive coefficients and multiple penalties.
method Pathwise optimization with accelerated proximal gradient descent and blockwise alternating optimization.
result Efficient computation of the full solution path for adaptive bridge estimators.
We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer's pathwise Itō calculus. Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategie…
Improves BED scalability for implicit models.
problem Designing experiments for implicit models with intractable data distributions.
method Hybrid gradient approach combining variational MI estimator, ES, and SGA.
result Significantly improves scalability of BED for implicit models.
Pathwise uniqueness shown for specific stochastic equations.
problem Stochastic Volterra equations with singular kernels and Hölder coefficients.
method Established pathwise uniqueness through Hölder continuity of coefficients.
result Pathwise uniqueness and existence of unique strong solutions.
Develops pathwise analysis for log-optimal portfolios using rough paths theory.
problem Analyzing stability and approximation of log-optimal portfolios.
method Pathwise approach based on càdlàg rough paths theory.
result Establishes pathwise stability and error estimates for log-optimal portfolios.
Develops portfolio theory without probabilistic analysis, focusing on pathwise decomposition.
problem Ensuring market viability without probabilistic assumptions.
method Uses pathwise decomposition and trend extractors to replace semimartingale decomposition.
result Growth-numéraire and viability equivalences are similar but not identical in pathwise setting.
A new approach to continuous-time universal portfolios using pathwise Itô calculus.
problem Continuous-time version of Cover's universal portfolio strategies.
method Pathwise Itô calculus approach to establish existence and properties of universal portfolio strategies.
result The universal portfolio strategy's portfolio value process is the average of all values of constant rebalanced strategies.
The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: {\it warm start initialization}, {\it active set updating}, and {\it …
We use pathwise Itô calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of Föllmer's pathwise Itô calculus and works for portfolios generated from functions that may depend on the current states of the market port…
Efficient inference for adaptive data with directional stability condition.
problem Efficient inference on scalar targets after adaptive data collection.
method Introduces directional stability, a weaker condition than i.i.d. data, and shows asymptotic normality and efficiency of estimators.
result Estimators remain asymptotically normal and semiparametrically efficient under directional stability.
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a path…
This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.
problem Expensive and unstable computation of hedge ratios from pathwise sensitivities.
method Develops reduced stochastic hedge ratios of the form φ_j^r = Σ_j^r ξ_j^q X_q, retaining sensitivity tensor through empirical averages.
result Two coefficient criteria are introduced to minimize pathwise residuals and satisfy moment equations.
The Monte Carlo pathwise sensitivities approach is well established for smooth payoff functions. In this work, we present a new Monte Carlo algorithm that is able to calculate the pathwise sensitivities for discontinuous payoff functions. Our main tool is to combine the one-step survival idea of Glasserman and Staum wi…
This paper gives several simple constructions of the pathwise Ito integral ∫0tφdω for an integrand φ and a price path ω as integrator, with φ and ω satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither φ nor ω are assumed to be paths of stochast…
This dissertation advances scalable Gaussian processes using iterative methods and pathwise conditioning.
problem The classical Gaussian process formulation is not scalable for large datasets and modern hardware.
method Combining iterative methods and pathwise conditioning to improve scalability.
result Significantly reduced memory requirements and facilitated application to larger datasets.
Second-order optimization speeds up deep hedging for complex options.
problem Hedging exotic options with market frictions in realistic markets.
method Second-order optimization scheme leveraging pathwise differentiability and Kronecker-factoring.
result Our method optimizes the policy in 1/4 the steps of standard optimization.
This work introduces efficient sampling methods for Gaussian processes by focusing on pathwise conditioning.
problem Intractable mathematical expressions in Gaussian process posteriors limit practical applications.
method Investigates a pathwise interpretation of conditioning to derive efficient sampling methods.
result Derives a general family of approximations that allow for efficient sampling of Gaussian process posteriors.
MuRiT efficiently computes multi-parameter persistence barcodes.
problem Efficient computation of multi-parameter persistent homology.
method Vietoris-Rips transformation to reduce multi-parameter to single-parameter computation.
result MuRiT computes pathwise persistence barcodes for multi-filtered flag complexes.
New algorithm reduces variance in Monte Carlo simulations using deep neural networks and policy gradients.
problem Reducing variance in Monte Carlo simulations for estimating function values.
method Optimal correlation search using deep neural networks and policy gradients.
result Optimal correlation function reduces variance by approximating and calibrating policy.
We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …
A new reinforcement learning method uses model derivatives to improve policy optimization.
problem Improving sample efficiency and performance in model-based reinforcement learning.
method Constructs an actor-critic algorithm that uses the pathwise derivative of the learned model and policy.
result Consistently more sample efficient and matches model-free algorithms' asymptotic performance.
We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical analysis, and an implied volatility consistent with options priced with the model. The…
Efficient estimators for smooth Hilbert-valued parameters with theoretical guarantees.
problem Estimating smooth Hilbert-valued parameters with theoretical guarantees.
method Pathwise differentiable Hilbert-valued parameters, efficient influence functions, regularized one-step estimators.
result Theoretical guarantees for efficient estimators even when nuisance functions are arbitrary.
We consider a class X of continuous functions on [0,1] that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in X admits a linear pathwise quadratic variatio…
Study shows how market firm capitalization models converge to stochastic PDE solutions.
problem Understanding convergence of rank-based models with common noise to stochastic PDE solutions.
method Analysis of mean field limit, martingale problem, and pathwise entropy solutions.
result Empirical cumulative distribution function converges to solution of a stochastic PDE under certain conditions.
Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is α-Hölder …
Exact simulation method for market impact estimation under various execution strategies.
problem Estimating market impact from observed price trajectories under different execution strategies.
method Conditional simulation of point processes under perturbed intensities.
result Exact, event-driven algorithm for reconstructing counterfactual paths.
Previously, the exploding gradient problem has been explained to be central in deep learning and model-based reinforcement learning, because it causes numerical issues and instability in optimization. Our experiments in model-based reinforcement learning imply that the problem is not just a numerical issue, but it may …
This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; t…
New method reduces errors in pricing and sensitivities for discontinuous payoffs.
problem Errors in pricing and sensitivities for discontinuous payoffs in digital and barrier options.
method Alternative methods for estimating sensitivities, including likelihood ratio and hybrid methods.
result New methods substantially reduce test errors in prices and sensitivities.
Score function estimators improve k-subset sampling efficiency.
problem Efficiently sampling k-subsets in machine learning tasks. method Revisit score function estimators, using discrete Fourier transform and control variates.
result Efficient and unbiased gradient estimates for k-subset sampling. Paper improves variance control in importance weighted variational bounds.
problem Improving the variance of gradient estimators for IWAE.
method Develops a novel control variate that grows SNR as √K for large K.
result Empirically, the method yields superior variance reduction for generative models.
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and tail asymptotics for diffusions, as well as for option prices and realised vari…
New method reduces training time for deep hedging networks.
problem Challenges in training deep hedging networks with large batch sizes.
method Integrates topological features to reduce batch sizes.
result Practical training of deep hedging models without sacrificing performance.
Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.
problem Computational challenges in high-dimensional ℓ1 penalized quantile regression. method Pathwise coordinate descent algorithm to solve exact coordinatewise minimum of the nonsmooth loss function.
result Algorithm runs faster than existing alternatives and maintains estimation accuracy.
Analysis of cross-validation for early-stopped gradient descent in high-dimensional regression.
problem Inconsistency of GCV for early-stopped GD in high-dimensional least squares regression.
method Theoretical analysis of GCV and LOOCV applied to early-stopped GD in high-dimensional least squares regression.
result LOOCV converges uniformly to the prediction risk of early-stopped GD, while GCV is generically inconsistent.
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
Agent maximizes utility with pathwise constraint on portfolio value.
problem Maximizing utility with a pathwise constraint on portfolio value.
method Max-plus decomposition for supermartingales, Black-Scholes-Merton model.
result Explicit form of optimal terminal wealth and process involved.
We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended…
Framework for training stochastic spiking neural networks with rough signals.
problem Training stochastic spiking neural networks with noisy spike timing and dynamics.
method Rough path theory and signature kernels for gradient computation.
result Pathwise gradients of SSNNs' trajectories and event times exist and satisfy a recursive relation.