arXiv research

New algorithm reduces pricing error by a factor of T^2/3.

Study proves existence and uniqueness for differential equations with non-Lipschitz coefficients.

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing spars…

New algorithms for online learning without boundedness or Lipschitz loss assumptions.

Paper proves convergence for private FL on non-Lipschitz convex objectives using normalization instead of clipping.

Extends involutivity to non-Lipschitz subbundles and proves the Frobenius Theorem.

We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the opt…

New bounds for online portfolio selection without smoothness assumptions.

Paper analyzes robustness of non-Lipschitz networks, proving powerful adversarial attacks but offering solutions.

Improved MLMC method for barrier options with non-Lipschitz coefficients.

Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to generalize the concept of Lipschitz smoothness condition to the relative smoothn…

New method models fat-tailed distributions with anisotropic tail-adaptive flows.

The CEV model is given by the stochastic differential equation $X_t=X_0+\int_0^tμX_sds+\int_0^tσ(X^+_s)^pdW_s$, $\frac{1}{2}\le p<1$. It features a non-Lipschitz diffusion coefficient and gets absorbed at zero with a positive probability. We show the weak convergence of Euler-Maruyama approximations $X_t^n$ to the proc…

We prove strong existence and uniqueness, and Hölder regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an approximation of the process by a sequence of semimartingales with regularised ke…

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 …

We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. T…

Demand variance can result in a mismatch between planned supply and actual demand. Demand shaping strategies such as pricing can be used to shift elastic demand to reduce the imbalance. In this work, we propose to consider elastic demand in the forecasting phase. We present a method to reallocate the historical elastic…

The paper proposes a new model to better estimate demand from censored data.

Demand functions for goods are generally cyclical in nature with characteristics such as trend or stochasticity. Most existing demand forecasting techniques in literature are designed to manage and forecast this type of demand functions. However, if the demand function is lumpy in nature, then the general demand foreca…

Transport demand is highly dependent on supply, especially for shared transport services where availability is often limited. As observed demand cannot be higher than available supply, historical transport data typically represents a biased, or censored, version of the true underlying demand pattern. Without explicitly…

Study improves cross-modal bike-share and transit demand prediction.

We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general …

A new metric optimizes forecasts for lumpy, intermittent demand.

Statistical arbitrageurs have inelastic demand, contrary to classical models.

Implementing a set of microeconomic criteria, we develop price dynamics equations using a function of demand/supply with key symmetry properties. The function of demand/supply can be linear or nonlinear. The type of function determines the nature of the tail of the distribution based on the randomness in the supply and…

Recommending the right products is the central problem in recommender systems, but the right products should also be recommended at the right time to meet the demands of users, so as to maximize their values. Users' demands, implying strong purchase intents, can be the most useful way to promote products sales if well …

Novel probabilistic models forecast residential heating and electricity demand at hourly resolution.

Study on non-negative solutions for stochastic Volterra equations with jumps.

Two neural network models analyze bus system efficiency and demand.

Heat demand prediction is a prominent research topic in the area of intelligent energy networks. It has been well recognized that periodicity is one of the important characteristics of heat demand. Seasonal-trend decomposition based on LOESS (STL) algorithm can analyze the periodicity of a heat demand series, and decom…

We study online optimization of smoothed piecewise constant functions over the domain [0, 1). This is motivated by the problem of adaptively picking parameters of learning algorithms as in the recently introduced framework by Gupta and Roughgarden (2016). Majority of the machine learning literature has focused on Lipsc…

Intermittent demand, where demand occurrences appear sporadically in time, is a common and challenging problem in forecasting. In this paper, we first make the connections between renewal processes, and a collection of current models used for intermittent demand forecasting. We then develop a set of models that benefit…

Proposes a new model for more accurate demand forecasting considering dynamic contextual information.

The paper tackles ride-hailing fleet repositioning with a calibrated demand approach.

Taxi demand prediction has recently attracted increasing research interest due to its huge potential application in large-scale intelligent transportation systems. However, most of the previous methods only considered the taxi demand prediction in origin regions, but neglected the modeling of the specific situation of …

We consider a firm that sells products over $T$ periods without knowing the demand function. The firm sequentially sets prices to earn revenue and to learn the underlying demand function simultaneously. A natural heuristic for this problem, commonly used in practice, is greedy iterative least squares (GILS). At each ti…

Study on inventory control with changing demand, proposing adaptive algorithms.

Model predicts trading strategies based on latent demand and price impact.

Paper optimizes demand aggregation for low-level electricity markets.

MaxCOSD algorithm tackles non-i.i.d. demands and stateful dynamics in online inventory control.

Multi-step passenger demand forecasting is a crucial task in on-demand vehicle sharing services. However, predicting passenger demand over multiple time horizons is generally challenging due to the nonlinear and dynamic spatial-temporal dependencies. In this work, we propose to model multi-step citywide passenger deman…

The paper tackles revenue management with time-varying demand using posterior sampling.

Unified framework for intermittent demand forecasting using renewal processes.

Study shows how China's stock market reflects economic demand changes during COVID-19.

A new macroscopic market making model connects market making and optimal execution.

New framework estimates demand responses across multiple contexts with limited price variation.

This study develops an online predictive optimization framework for dynamically operating a transit service in an area of crowd movements. The proposed framework integrates demand prediction and supply optimization to periodically redesign the service routes based on recently observed demand. To predict demand for the …