A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
DGKIP extends KIP for dataset distillation without bi-level optimization.
Several recently proposed architectures of neural networks such as ResNeXt, Inception, Xception, SqueezeNet and Wide ResNet are based on the designing idea of having multiple branches and have demonstrated improved performance in many applications. We show that one cause for such success is due to the fact that the mul…
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…
In this paper, we extend the T-duality isomorphism by Gualtieri and Cavalcanti, from invariant exact Courant algebroids, to exotic exact Courant algebroids such that the momentum and winding numbers are exchanged, filling in a gap in the literature.
This note provides a novel, simple analysis of the method of conjugate gradients for the minimization of convex quadratic functions. In contrast with standard arguments, our proof is entirely self-contained and does not rely on the existence of Chebyshev polynomials. Another advantage of our development is that it clar…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a…
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path , might be strictly greater than the …
In this note, we fill in a gap in the literature by proving that the Teichmueller modular groups (mapping class groups) are not Poincare duality groups and the complexes of curves of surfaces have infinite homotopy type (i.e. are not homotopy equivalent to a finite CW-complex).
Study resolves duality gap in optimal consumption with random income termination.
Paper tackles fast convergence for non-convex strongly-concave min-max problems.
Using our earlier proposal for Ramond-Ramond fields in an H-flux on loop space, we extend the Hori isomorphism of Bouwknegt-Evslin-Mathai from invariant differential forms, to invariant exotic differential forms such that the momentum and winding numbers are exchanged, filling in a gap in the literature. We also extend…
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
We propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full Frank-Wolfe algorithm. We also show that, when applied to the d…
Extends portfolio optimization with two quasiconvex risk measures.
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to incorporate prior knowledge and impose desired structural and statistical proper…
Study stability of contingent claim solutions under probabilistic perturbations.
Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the so-called for the Lasso. Based on duality gap considerations, our new rules create safe test regions whose d…
Optimal transport reformulates multiple quantile hedging problem.
Study potential computational gaps in symmetric binary perceptrons using fl-RDT.
Study shows cooperation can reduce investment risk and price gaps.
New approach shapes error distribution in long-term forecasting.
Paper analyzes complexity of PSGLA for sampling log-concave distributions.
We develop a dual-control method for approximating investment strategies in incomplete environments that emerge from the presence of trading constraints. Convex duality enables the approximate technology to generate lower and upper bounds on the optimal value function. The mechanism rests on closed-form expressions per…
New approach reduces simulator exploitation by learning robust models.
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.
In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we prove that th…
Epoch gradient descent method (a.k.a. Epoch-GD) proposed by Hazan and Kale (2011) was deemed a breakthrough for stochastic strongly convex minimization, which achieves the optimal convergence rate of with iterative updates for the {\it objective gap}. However, its extension to solving stochastic min-max pr…
High dimensional regression benefits from sparsity promoting regularizations. Screening rules leverage the known sparsity of the solution by ignoring some variables in the optimization, hence speeding up solvers. When the procedure is proven not to discard features wrongly the rules are said to be \emph{safe}. In this …
Theoretical analysis of MCR for improving imputation quality in partially observed data.
Stable commutator length scl_G(g) of an element g in a group G is an invariant for group elements sensitive to the geometry and dynamics of G. For any group G acting on a tree, we prove a sharp bound scl_G(g)>=1/2 for any g acting without fixed points, provided that the stabilizer of each edge is relatively torsion-fre…
We consider the classical optimal dividends problem under the Cramér-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value functi…
Paper tackles constrained learning with non-convex losses, overcoming challenges with new approach.
New approach reduces simulator exploitation by improving strategic robustness.
Develops a regression approach for solving MDPs with general state and action spaces.
Deep learning struggles with out-of-distribution data, so this paper tackles domain generalization.
In high dimensional regression settings, sparsity enforcing penalties have proved useful to regularize the data-fitting term. A recently introduced technique called screening rules propose to ignore some variables in the optimization leveraging the expected sparsity of the solutions and consequently leading to faster s…
Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamentally dif…
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing IHT-style methods are designed for sparse minimization in primal form. It remains open t…
Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning~(RL), these problems are addressed by (i)~designing a reward function that simultaneously…
We consider a financial market with one riskless and one risky asset. The super-replication theorem states that there is no duality gap in the problem of super-replicating a contingent claim under transaction costs and the associated dual problem. We give two versions of this theorem. The first theorem relates a numéra…
New framework for DP-SMO with near-optimal privacy-loss trade-off.
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options are traded at certain maturities, and the forward price implied by these option pr…
New graph feedback model for bandits with improved regret bounds.
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results. Coping with the infinite dimensionality and non-convexity of these problems typica…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literatur…
Convex sparsity-inducing regularizations are ubiquitous in high-dimensional machine learning, but solving the resulting optimization problems can be slow. To accelerate solvers, state-of-the-art approaches consist in reducing the size of the optimization problem at hand. In the context of regression, this can be achiev…
The regularization path of the Lasso can be shown to be piecewise linear, making it possible to "follow" and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is exponential in the number of variables. We then oppose this pessimistic result to a…