The paper extends NUP representations to factor graphs for better estimation.
problem Nontrivial model-based estimation problems.
method Augmenting factor graphs with convex-dual variables and NUP representations; proposing a new iterative algorithm.
result A new dual algorithm for state space problems.
A new method for solving complex financial equations.
problem Solving complex financial equations with nested conditional expectations.
method Pathwise iteration for backward SDEs.
result Computes and iteratively improves upper and lower bounds on the true solution.
New algorithm draws Julia sets for Möbius semigroups not previously possible.
problem Drawing Julia sets for Möbius semigroups with non-thick attractors.
method Backward Iteration algorithm extension to Möbius semigroups.
result Julia sets of Möbius semigroups can be drawn, including those not thick attractors.
We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the pictures of the Julia sets, previously proven to work in the context of iteration of a rational map of degree two or more, extends to finitely gene…
Proposes a new algorithm for k-means clustering using stochastic backward Euler.
problem Improving k-means clustering performance and robustness. method Implicit gradient descent with stochastic backward Euler iteration.
result The algorithm provides better clustering results compared to traditional k-means. Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
problem Proving convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
method Differentiation-based approach to handle Z process, uniformly controlling Lipschitz continuity of decoupling fields.
result Proves convergence of Markovian iteration method for FBSDEs with fully coupled drift and Z process.
New method shows how order of gradient updates impacts stability and convergence in deep learning.
problem Training deep learning models can be unstable and computationally expensive.
method Theoretical analysis and experiments with backward-SGD.
result The order of gradient updates affects stability and convergence, leading to improved performance.
Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show tha…
Spherical T-duality for iterated sphere bundles
problem T-duality for iterated sphere bundles
method Repackaging cohomological data into Massey products
result Found T-dual iterated sphere bundles associated to Massey products
Proves global well-posedness for superquadratic BSDEs without Markovian assumption.
problem Global well-posedness of multidimensional superquadratic BSDEs without Markovian assumption.
method Interplay between local well-posedness of FBSDEs and backward iterations of superquadratic BSDEs.
result Global well-posedness of superquadratic BSDEs proved.
New FPI layers enable efficient backpropagation in deep networks.
problem Designing deep neural networks to handle complex constraints.
method Fixed-point iteration layers for forward and backward propagation.
result Backward FPI layer simplifies gradient calculation without explicit Jacobian.
Study spherical T-duality and Massey products in iterated sphere bundles.
problem Understanding spherical T-duality and Massey products in iterated sphere bundles.
method Analyzing Gysin sequences and Massey products to find T-dual iterated sphere bundles.
result For certain iterated sphere bundles, spherical T-duality can be represented by Massey products.
Proposes EM-C algorithm for solving stochastic control problems.
problem Solving multi-period finite time horizon stochastic control problems.
method Sequentially updates control policies using Monte Carlo simulation in a forward-backward manner.
result Demonstrates effectiveness in monopoly pricing and real business cycle studies.
New algorithms improve direction finding using prior signal knowledge.
problem Efficiently estimate signal direction from sensor data.
method Multi-step knowledge-aided iterative conjugate gradient algorithms.
result MS-KAI-CG algorithms outperform existing techniques in simulations.
New PDEs model implied volatility without prior knowledge.
problem Modeling implied volatility without prior knowledge.
method Derived backward and forward nonlinear PDEs, discussed initial and boundary conditions, solved numerically.
result Solved PDEs for implied volatility of positive stock price contingent claims.
Accelerates Birkhoff projection for manifold-constrained hyper-connections with high accuracy and speed.
problem Inaccurate and slow Birkhoff projection in mHC implementations.
method Dual formulation, Newton's method, implicit differentiation, warp-level CUDA kernel.
result Substantial speedups and accuracy improvements in doubly stochastic projections.
PFBP algorithm speeds up feature selection in big data.
problem Feature selection in high-dimensional and/or large sample size data.
method PFBP algorithm partitions data and uses local computations with early decisions.
result Asymptotic optimality for causal networks, super-linear speedup, linear scalability.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
problem Nonlinear filtering problem in high-dimensional systems.
method Iterative and adaptive meshfree approach using forward backward SDE and KDE.
result Rigorous convergence analysis provided, supporting empirical results.
Paper generalizes extragradient methods for solving equations and inclusions with improved convergence rates.
problem Solving equations and inclusions using extragradient methods.
method Unified and generalized extragradient methods for a broader class of algorithms, analyzing sublinear convergence rates.
result Unified and improved convergence results for various extragradient variants.
New variance-reduction methods solve stochastic composite inclusions.
problem Solving nonmonotone stochastic composite inclusions.
method Developed unbiased and biased variance-reduced estimators for FRBS method.
result Achieved best oracle complexities for finite-sum and expectation settings.
New method improves adversarial training efficiency and robustness.
problem High computational costs and lack of stability in adversarial training.
method Backward smoothing for randomized smoothing of random initialization.
result Our method achieves similar model robustness as state-of-the-art methods but with significantly less training time.
New methods solve SPDEs for financial derivative pricing.
problem Deriving the price of financial derivatives using SPDEs.
method Developed a conditional Feynman-Kac formula to solve SPDEs.
result Established new numerical methods for mixed Monte-Carlo PDEs.
New deep learning method solves complex BSDEs efficiently.
problem Solving high-dimensional nonlinear BSDEs.
method Reformulate as global optimization, approximate solution with deep neural network, globally minimize quadratic local loss functions.
result Demonstrated effectiveness on various high-dimensional nonlinear BSDEs, including finance applications.
Faster LSTM training with structured sparsity.
problem Slower LSTM training due to the complexity of the backward pass.
method Structured sparsity in LSTM gate gradients to speed up the backward pass.
result Up to 45% faster LSTM training on modern GPUs.
We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large number of optimization problems, thus it is not scalable for large-size problems…
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may …
Method combines deep learning and elicitability for solving complex stochastic equations.
problem Solving McKean-Vlasov FBSDEs with common noise.
method Combines Picard iterations, elicitability, and deep learning.
result Validated on systemic-risk model and extended to quantile-mediated interactions.
A new family of momentum coefficients improves the convergence rate of accelerated algorithms.
problem Improving the convergence rate of accelerated gradient methods for strongly convex functions.
method Introducing a family of controllable momentum coefficients for forward-backward accelerated methods.
result Established a controllable $O\left(1/k^{2α}
ight)$ convergence rate for the NAG-α method. Efficiently samples complex distributions using tensor train format.
problem Sampling from high-dimensional complex probability densities efficiently.
method Integrates tensor train format with backward stochastic differential equations (BSDEs) for fast, robust, and accurate sampling.
result Improved efficiency in sampling from challenging target distributions.
New insights show NAG and FISTA converge linearly without knowing strong convexity modulus.
problem Understanding linear convergence of NAG and FISTA without strong convexity modulus knowledge.
method High-resolution ODE framework, dynamically adapting kinetic energy coefficient.
result NAG and FISTA demonstrate linear convergence without requiring strong convexity modulus knowledge.
Tensor trains simplify solving complex PDEs efficiently.
problem Solving high-dimensional parabolic PDEs using traditional methods is computationally infeasible.
method Reformulate PDEs as backward stochastic differential equations and use tensor train format for compression and efficient computation.
result Tensor train methods achieve a good balance between accuracy and computational efficiency.
Valuation of Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss of a default event without any recovery, is one of the key elementsfor pricing CVA. This pap…
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization p…
The paper applies deep learning to solve complex control problems.
problem Solving stochastic control problems on finite horizons.
method Deep neural networks algorithms for control learning.
result Performance of algorithms on various control problems demonstrated.
Two accelerated extragradient methods converge at O(1/k) rate for co-hypomonotone inclusions.
problem Solving co-hypomonotone inclusions with sum of Lipschitz and multivalued operators.
method Developed two Nesterov's accelerated extragradient methods for co-hypomonotone inclusions.
result Achieve O(1/k) last-iterate convergence rates on the residual norm. CMCD sampler connects transport and variational inference for efficient sampling.
problem Efficient sampling and generative modeling in Bayesian computation.
method Developed a principled framework using divergences on path space, CMCD sampler with adaptive dynamics.
result CMCD sampler outperforms competing approaches across various experiments.
New method uses zeroth-order queries to approximate proximal sampling efficiently.
problem Approximating proximal sampling with zeroth-order information.
method Direct simulation of heat flow dynamics, treating intermediate distribution as Gaussian mixture.
result Inherits exponential convergence under isoperimetric conditions, avoids rejection sampling.
A framework for robust exploration in reinforcement learning under ambiguity.
problem Optimal stopping under ambiguity in reinforcement learning.
method Continuous-time robust reinforcement learning framework using g-expectation and backward stochastic differential equations. result Constructs a robust exploratory stopping time approximating the optimal stopping time under ambiguity.
A new method estimates Schrödinger bridges without iterative simulations or neural networks.
problem Estimating the time-dependent drift between two probability distributions.
method Solving the static entropic optimal transport problem and modifying the potentials.
result The Sinkhorn bridge method provably estimates Schrödinger bridges with a rate of convergence dependent on the target measure's intrinsic dimensionality.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
problem Nonlinear Forward Backward Stochastic Differential Equations (FBSDE) with terminal conditions.
method Backward deep BSDE method applied to FBSDE with nonlinear generators and random initial conditions.
result Derives exact and Taylor-based approximations for time-stepping nonlinear BSDEs.
One-step diffusion samplers reduce sampling time and computational costs.
problem Efficient sampling from complex distributions.
method One-step diffusion, self-distillation, deterministic flow.
result Achieves competitive sample quality with fewer evaluations.
New method uses tensor trains for efficient PDE approximation.
problem High-dimensional PDEs and the curse of dimensionality.
method Tensor trains and backward stochastic differential equations for parabolic PDEs.
result Achieves a favorable trade-off between accuracy and computational efficiency.
Optimal trading strategy derived for nonlinear price impact models.
problem Optimal trading with nonlinear price impact induced by alpha signals.
method Variational approach, nonlinear Fredholm equation, iterative scheme.
result Existence and uniqueness of optimal trading strategy under monotonicity condition.
U-turn chains improve sampling from complex distributions.
problem Sampling from high-dimensional learned distributions.
method Iterative forward-backward diffusion steps with Metropolis-Hastings correction.
result Minimal U-turn dynamics exhibit phase transitions and layer-ordering inversion.
Develops variance-reduced methods for solving generalized equations.
problem Solving a class of generalized equations, including minimization, minimax, and variational inequalities.
method Integrates accelerated operator splitting, fixed-point methods, and variance reduction techniques.
result Achieves both O(1/k2) and o(1/k2) convergence rates on the expected squared norm of the FBS residual. Improves sequence generation by training a backward network.
problem Generating long-term dependencies in sequence models.
method Train a backward recurrent network to predict states of a forward model.
result Achieves 9% relative improvement in speech recognition and significant improvement in caption generation.
Adaptive step size improves online learning performance.
problem Tedious tuning of step size in online learning algorithms.
method Adapt step size by gradient descent on the step size itself.
result Online adaptation reduces performance variability.
Shows uniqueness of mean curvature flow in higher dimensions.
problem Backwards uniqueness of mean curvature flow.
method Analysis of mean curvature flow with bounded second fundamental form.
result Proves backwards uniqueness in arbitrary codimension.