A new one-point feedback scheme improves ZO algorithms for black-box optimization.
problem Optimizing black-box functions without gradient information.
method Proposes a one-point feedback scheme to estimate gradients using residuals.
result Matches query complexity of two-point schemes for deterministic Lipschitz functions.
Deep, wide ConvResNets can approximate functions and their smoothness.
problem Function approximation and smoothness in deep networks.
method Analyzing ConvResNets, proving their ability to approximate functions and their smoothness.
result Large ConvResNets can approximate functions and exhibit sufficient first-order smoothness.
The aim of this article is to generalize in several variables some formulae for Eisenstein series in one variable. For example the formula 2ζ(2k)=(2π)2k(2k)!B2k=Resz=0(z2k(1−ez)1) for the values of zeta functions at even integers in functions of Bernoulli numbers. A. Szenes proved …
New method improves deep policy gradient algorithms by learning relative state values.
problem High sample complexity and instability in policy gradient methods.
method Uses a new state-value function approximation based on residual variance.
result Empirical improvement across diverse continuous control tasks and algorithms.
CEFOL uses deep learning for dynamic programming with recursive utility.
problem Challenges in solving dynamic programming problems with recursive utility.
method Introduces a separate neural network for certainty equivalent, uses first-order optimality conditions to learn value and policy functions.
result CEFOL achieves high accuracy in learning value and policy functions, matching VFI benchmarks.
We develop a polynomial method to optimize trading in markets with transaction costs.
problem Optimizing trading strategies in markets with proportional transaction costs.
method Polynomial approximation of the residual value function to determine optimal trading strategies.
result Identify the trade-off between trading frequency and trade sizes for satisfactory agreement with theoretically optimal strategies.
The Wodzicki residue and the cut-off integral extend to classical symbol-valued forms. We show that they obey a Stokes' type property and that the extended Wodzicki residue can be interpreted as a complex residue like the ordinary one. In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact forms) o…
Deep residual networks can approximate any continuous function using control theory.
problem Universal approximation capabilities of deep residual neural networks.
method Relating residual networks to control systems and using Lie algebraic techniques.
result Deep residual networks with adequately deep layers can approximate any continuous function on a compact set.
This paper improves bond market making by adjusting hit-ratios for client flow quality.
problem Economic misleading of raw hit-ratios in corporate bond market making.
method Stochastic-control framework with residual-quality-adjusted hit-ratio.
result Optimal quotes decompose into various components, improving service/economics frontier.
Develops efficient inference for noise heterogeneity in machine learning models.
problem Downstream procedures based on residuals can be biased in additive noise models.
method Semiparametrically efficient inference using a novel Hilbert-valued one-step estimator.
result Constructs tests and confidence intervals for residual independence and goodness of fit.
KBB algorithm reduces sample complexity for policy evaluation in general state spaces.
problem Policy evaluation in large state spaces with high sample complexity.
method Alternates between fitting Bellman residual and estimating value function via adaptive feature set growth.
result Super-linear convergence rates demonstrated, with reductions in sample complexity.
This paper aims at theoretically and empirically comparing two standard optimization criteria for Reinforcement Learning: i) maximization of the mean value and ii) minimization of the Bellman residual. For that purpose, we place ourselves in the framework of policy search algorithms, that are usually designed to maximi…
We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the input images. We work with ResNet-56 and ResNet-110 trained on the CIFAR-10 dat…
The paper analyzes how to combine self-protection and self-insurance for risk reduction.
problem Combining self-protection and self-insurance for risk reduction when market insurance is absent.
method The approach uses Value-at-Risk and Tail Value-at-Risk to evaluate residual risk and solves the problem using isoquant geometry based on marginal-balance curves.
result The analysis identifies the conditions under which self-protection and self-insurance behave as substitutes or complements.
A method to reduce bias in model-based policy evaluation by shifting operators.
problem Bias in value function computation from noisy estimated models.
method Operator shifting method to reduce the residual norm error.
result The shifting factor is always positive and upper bounded by $1+O\left(1/n
ight)$.
Study tight offline learning bounds for linear MDPs using variance information.
problem Understanding statistical limits with linear function representations in offline reinforcement learning.
method Variance-aware pessimistic value iteration (VAPVI) that reweights Bellman residuals based on estimated variances.
result Improved offline learning bounds expressed in terms of system quantities.
Leasing is a popular channel to market new cars. Pricing a leasing contract is complicated because the leasing rate embodies an expectation of the residual value of the car after contract expiration. To aid lessors in their pricing decisions, the paper develops resale price forecasting models. A peculiarity of the leas…
A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just the residual of the previous layer's output and the target output. Thus, we should…
Temporal difference learning and Residual Gradient methods are the most widely used temporal difference based learning algorithms; however, it has been shown that none of their objective functions is optimal w.r.t approximating the true value function V. Two novel algorithms are proposed to approximate the true value…
Researchers compute Wodzicki residue for pseudo-differential operators on compact Lie groups.
problem Computing the Wodzicki residue for pseudo-differential operators on compact Lie groups.
method Analytic continuation of traces and matrix-valued symbols.
result Main theorem complementary to [2], removing ellipticity hypothesis.
The paper derives spectral (0,4)-tensor functionals using the noncommutative residue.
problem Deriving spectral (0,4)-tensor functionals on compact spin manifolds.
method Using four one-forms and the Dirac operator, the noncommutative residue is applied to even-dimensional compact spin manifolds.
result Spectral (0,4)-tensor functionals are extended to a general spectral triple.
Field theory explains optimal scaling in ResNets for signal propagation.
problem Understanding optimal scaling parameter for ResNet performance.
method Finite-size field theory for ResNets to study signal propagation and scaling.
result Analytical expressions for optimal scaling parameter, independent of other hyperparameters.
Jeffrey and Kirwan suggested expressions for intersection pairings on the reduced space of a Hamiltonian G-space in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a quasi-Hamiltonian SU(2)-space. The definition of quasi-Hamiltonian G-spaces was recently …
Batch normalization makes deep residual networks train faster.
problem Training deep residual networks with large depths.
method Downscaling the residual branch by a normalizing factor early in training.
result Normalized residual blocks compute functions close to the identity function early in training.
Examines a new type of analytic torsion on Riemannian manifolds.
problem Analyzing a new trace formula for Riemannian manifolds.
method Uses residue-trace instead of spectral zeta function quasi-trace.
result Defines and examines the residue analytic torsion.
The paper studies residues of manifolds and their applications in geometry.
problem Understanding the residues of manifolds and their geometric implications.
method Analytic continuation and Möbius invariance of residues, introduction of relative and weighted residues.
result Scalar curvature, mean curvature, and Euler characteristic can be expressed in terms of residues.
Wasserstein gradient boosting predicts probability distributions for supervised learning.
problem Distribution-valued supervised learning where outputs are probability distributions.
method Fits a new weak learner to Wasserstein gradients of loss functionals of probability distributions.
result Superior performance in probabilistic prediction compared to existing methods.
A well known result on pseudodifferential operators states that the noncommutative residue (Wodzicki residue) of a pseudodifferential projection vanishes. This statement is non-local and implies the regularity of the eta invariant at zero of Dirac type operators. We prove that in a filtered algebra the value of a proje…
Deep neural net solves multi-agent optimal trading problem.
problem Optimal trade execution for multiple agents and assets.
method Residual U-net with self-attention for viscosity solution approximation.
result Neural network approach outperforms finite difference methods.
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Estimating the residual Monge-Ampère mass of symmetric plurisubharmonic functions with isolated singularities.
method Utilized Sasakian geometry to derive estimates on the residual mass in relation to Lelong numbers.
result Partially resolved the zero mass conjecture by Guedj and Rashkovskii.
New spectral functionals related to noncommutative residue and torsion Dirac operators.
problem Spectral functionals and Dirac operators with torsion.
method Noncommutative residue and Dirac operators with torsion.
result Extension of spectral functionals to noncommutative realm with torsion.
We extend the calculus of adiabatic pseudo-differential operators to study the adiabatic limit behavior of the eta and zeta functions of a differential operator δ, constructed from an elliptic family of operators indexed by S1. We show that the regularized values η(δt,0) and tζ(δt,0) are smooth functions of …
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Analyzing the residual Monge-Ampère mass of symmetric plurisubharmonic functions.
method Proved zero mass for functions with zero Lelong number at origin and S1-invariance. result Zero mass conjecture answered for symmetric functions.
Study of η invariants on lens spaces detects distinctions invisible to ordinary η.
problem Detecting distinctions in η invariants on lens spaces. method Spin-Fourier residues and equivariant η invariants. result Second derivative of the residual η germ is nonzero for some lens spaces. Let M be a compact surface, either orientable or non-orientable. We study the lower central and derived series of the braid and pure braid groups of M in order to determine the values of n for which B\_n(M) and P\_n(M) are residually nilpotent or residually soluble. First, we solve this problem for the case where M is …
Residual networks with block width max(d_x, d_y) approximate all functions.
problem Achieving universal approximation with residual networks.
method Established bounds on block width for different activation functions.
result Minimum block width for universal approximation is max(d_x, d_y) with inner width 1.
The purpose of this paper is to present the construction of a canonical determinant functional on elliptic pseudodifferential operators associated to the Guillemin-Wodzicki residue trace. The resulting functional is multiplicative, a local invariant, and not defined by a regularization procedure. The residue determinan…
Wide residual networks generalize well with uniform convergence to RNTK as width increases.
problem Understanding the generalization ability of wide residual networks.
method Uniform convergence of residual network kernel to residual neural tangent kernel (RNTK).
result Generalization error converges to kernel regression error with respect to RNTK.
Extends spectral Einstein functionals computation to 4D spin manifolds with boundary.
problem Computing spectral Einstein functionals for 4D spin manifolds with boundary.
method Generalizes Dabrowski's results to 4D spin manifolds with boundary using noncommutative residue.
result Generalized spectral Einstein functionals computation for 4D spin manifolds with boundary.
VA-OPE improves OPE by incorporating variance information, achieving tighter error bounds.
problem Estimating value function of a target policy from offline data collected by a behavior policy.
method Proposes VA-OPE, an algorithm that reweights Bellman residual using estimated variance of the value function.
result Achieves a tighter error bound than the best-known result.
Promotes spectral functionals to noncommutative fields and proves a theorem.
problem Spectral functionals on noncommutative fields and manifolds with boundary.
method Carries out promotion to spectral functionals, associates with noncommutative residue, and proves theorem.
result Proves Dabrowski-Sitarz-Zalecki type theorem for statistical de Rham Hodge operators on manifolds with boundary.
Multi-output is essential in machine learning that it might suffer from nonconforming residual distributions, i.e., the multi-output residual distributions are not conforming to the expected distribution. In this paper, we propose "Wrapped Loss Function" to wrap the original loss function to alleviate the problem. This…
This is a survey of recent results on zeta- and eta-function poles and values for realizations of Laplace- and Dirac-type operators defined by pseudodifferential projection boundary conditions (including the Atiyah-Patodi-Singer operator and its square). Section 1 recalls some useful results for ps.d.o.s on closed mani…
In this paper, we study Lipschitz-Fredholm vector fields on Bounded-Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if M is a connected smooth bounded-Fréchet-Finsler manifold endowed with a strengthened connection K and if ξ is a smooth Lipschitz-Fr…
Study on residual Monge-Ampère mass of complex functions with directional Lipschitz continuity.
problem Estimating the residual Monge-Ampère mass of plurisubharmonic functions.
method General decomposition formula under Sasakian structure, L1-apriori estimate, upper-bound estimate on residual mass. result Upper-bound estimate on residual mass for uniformly directional Lipschitz continuity confirmed.
Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual …
New method reveals true causal functions in nonlinear time series, not just scores.
problem Causal discovery in nonlinear time series often uses scalar edge scores, which hide true function-valued causal influence.
method Formalized function-valued causal influence for additive, contribution-decomposable architectures. Introduced a practical framework based on ICE for estimating causal response functions directly from trained models.
result Edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors.
New method for insurance valuation combining hedging and risk minimization.
problem Current insurance valuation methods do not reflect regulatory risk measures.
method Two-step hedging procedure using generalised regression.
result The method produces portfolios neutral to risk measures like VaR or expectiles.