New algorithm reduces pricing error by a factor of T^2/3.
problem Optimal pricing under non-Lipschitz demand with unknown jumps and atoms.
method Conservative-Markdown Redirect-UCB Pricing, combining estimation, probing, and redirection.
result Achieves optimal regret of O(T^2/3), matching lower bounds.
Study proves existence and uniqueness for differential equations with non-Lipschitz coefficients.
problem Existence and uniqueness for differential equations with non-Lipschitz coefficients.
method Relying on robust Itô integration, prove existence and uniqueness results.
result Existence and uniqueness for one-dimensional differential equations with non-Lipschitz coefficients.
Proves existence and uniqueness of solutions for complex stochastic equations.
problem Proving solutions for stochastic Volterra equations with singular kernels and non-Lipschitz coefficients.
method Approximation by semimartingales with regularised kernels, extending Yamada-Watanabe's theorem.
result Strong existence and uniqueness of solutions for a large class of stochastic Volterra equations.
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.
problem Online learning with unbounded domains and non-Lipschitz losses.
method Developed an algorithm with a specific regret bound and used it for saddle-point optimization.
result First algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses.
Paper proves convergence for private FL on non-Lipschitz convex objectives using normalization instead of clipping.
problem Lack of convergence results for differentially private federated learning with non-Lipschitz objectives.
method Developed a convergence result for private FL on smooth convex objectives without assuming Lipschitzness, using normalization instead of clipping.
result Normalization-based private FL algorithm converges better than clipping-based counterpart on smooth convex functions.
Extends involutivity to non-Lipschitz subbundles and proves the Frobenius Theorem.
problem Defining involutivity for non-Lipschitz subbundles and proving the Frobenius Theorem.
method Using generalized functions, the Frobenius Theorem is extended to log-Lipschitz subbundles with sharp regularity estimates.
result For log-Lipschitz involutive subbundles, there exists a homeomorphism with specific regularity properties.
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.
problem Online portfolio selection with non-Lipschitz, non-smooth losses.
method Data-dependent bounds using novel smoothness characterizations and FTRL with self-concordant regularizers.
result Achieves logarithmic regrets when data is 'easy' and sublinear worst-case regrets.
Paper analyzes robustness of non-Lipschitz networks, proving powerful adversarial attacks but offering solutions.
problem Adversarial attacks on deep networks, especially non-Lipschitz networks.
method Developed an attack model that abstracts the challenge of adversarial robustness, proving the power of such attacks and offering solutions.
result Proves powerful adversarial attacks on non-Lipschitz networks but offers solutions with abstention.
Improved MLMC method for barrier options with non-Lipschitz coefficients.
problem Efficiency improvement for barrier option pricing with non-Lipschitz diffusion.
method Interpolated Drift Implicit Euler MLMC method, Lamperti transformation, Brownian bridge technique.
result Improved efficiency of MLMC for barrier options with non-Lipschitz coefficients.
Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.
problem Robust control of SDEs with ambiguity parameters and non-Lipschitz coefficients.
method Existence and uniqueness of value function established through BSDEs with non-linear growth conditions.
result Existence and uniqueness of value function in proper space, verified through BSDEs.
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.
problem Gaussian-based variational inference fails to accurately capture tail decay in fat-tailed distributions.
method Improved theory on tails of flows, developed anisotropic tail-adaptive flows (ATAF).
result ATAF models tail-anisotropy, outperforming prior work on synthetic and real-world targets.
The CEV model is given by the stochastic differential equation Xt=X0+∫0tμXsds+∫0tσ(Xs+)pdWs, 21≤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 Xtn to the proc…
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…
Modeling shared mobility demand considering supply limitations.
problem Inaccurate demand predictions due to limited supply.
method Censored Gaussian Processes for demand modeling.
result Taking supply limitations into account improves demand predictions.
The paper proposes a new model to better estimate demand from censored data.
problem Challenges in inferring true demand from aggregate, censored data.
method Combines Tobit likelihood with graph diffusion process in Gaussian Processes.
result The new model produces more accurate out-of-sample predictions.
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…
Study improves cross-modal bike-share and transit demand prediction.
problem Cross-modal ripple effects in urban transportation demand.
method Transfer learning and stacked LSTM models for cross-modal demand prediction.
result Transfer learning models outperform unimodal models in cross-modal 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.
problem Inaccurate demand forecasts lead to suboptimal logistics and production.
method Developed a novel metric that considers both statistical and business aspects.
result The new metric yields more accurate predictions for lumpy and intermittent demand.
Paper develops deep models for forecasting intermittent demand.
problem Forecasting intermittent demand with sporadic occurrences.
method Uses deep neural networks to model conditional interdemand time and size distributions.
result Empirical validation of deep models for intermittent demand forecasting.
Statistical arbitrageurs have inelastic demand, contrary to classical models.
problem Understanding the demand elasticity of statistical arbitrageurs.
method Thirteen models from the literature and a quantitative equilibrium model.
result Aggregate demand remains inelastic even with statistical arbitrageurs.
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 …
Study on non-negative solutions for stochastic Volterra equations with jumps.
problem Existence and uniqueness of non-negative solutions for stochastic Volterra equations with jumps and non-Lipschitz coefficients.
method Developed a nonnegative approximation approach and used Yamada--Watanabe approximation technique for convergence proof.
result Established conditions for strong existence and pathwise uniqueness of non-negative solutions.
Novel probabilistic models forecast residential heating and electricity demand at hourly resolution.
problem Accurate hourly forecasting of residential heating and electricity demand.
method Probabilistic deep learning models trained on gas-heated region data.
result Significant improvement in forecast accuracy compared to NREL's ResStock model.
Two neural network models analyze bus system efficiency and demand.
problem Identify service gaps and quantify demand in public transportation.
method Two neural network models considering demographic data and metrics.
result Models can generalize to other cities' bus systems.
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…
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…
Proposes a new model for more accurate demand forecasting considering dynamic contextual information.
problem Traditional methods fail to capture spatio-temporal and dynamic contextual dependencies in demand forecasting.
method Integrates temporal, relational, spatial, and dynamic contextual dependencies using a Context Integrated Graph Neural Network (CIGNN).
result CIGNN outperforms state-of-the-art baselines in multi-step ahead demand forecasting.
The paper tackles ride-hailing fleet repositioning with a calibrated demand approach.
problem Repositioning idle supply before future demand is observed in ride-hailing.
method A predict-then-optimize approach using calibrated demand regimes, a similarity gate, and spatial queue-regret decomposition.
result The spatial gate reduces mean wait time to 82.3s compared to 85.3s for a hand-tuned similarity gate and 85.8s for a distributional-only baseline.
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.
problem Inventory control with non-stationary demand distributions.
method Adaptive online algorithms optimizing base-stock policies.
result Sharp separation in adaptability across different inventory models.
Model predicts trading strategies based on latent demand and price impact.
problem Predicting strategic trading behavior of investors with private targets.
method Equilibrium model of dynamic trading, learning, and pricing by strategic investors.
result Trading strategies are a combination of target following, liquidity provision, and front-running based on latent demand and price pressure.
Paper optimizes demand aggregation for low-level electricity markets.
problem Accurate short-term load forecasting at low aggregation levels for market participants.
method Probabilistic portfolio optimization of residential households' demand using ARMA-GARCH models or KDE forecasts.
result Seasonal Residual approach outperforms others in accuracy and efficiency.
MaxCOSD algorithm tackles non-i.i.d. demands and stateful dynamics in online inventory control.
problem Managing inventory with non-i.i.d. demands and stateful dynamics.
method MaxCOSD, an online algorithm with provable guarantees for non-degeneracy assumptions.
result MaxCOSD achieves optimal performance for non-i.i.d. demands and stateful dynamics.
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.
problem Maximizing revenue in real-time applications with unknown and time-varying demand.
method Episodic generalization of RM problem, posterior sampling algorithm for linear programming optimization.
result The proposed algorithm outperforms other methods and is comparable to the optimal policy in hindsight.
Unified framework for intermittent demand forecasting using renewal processes.
problem Intermittency in demand forecasting.
method Unified framework based on extensions of discrete-time renewal processes.
result Efficacy demonstrated in forecasting practice with favorable predictive accuracy.
A new macroscopic market making model connects market making and optimal execution.
problem Connecting market making and optimal execution problems.
method Using continuous processes for orders, the model bridges the gap between market making and optimal execution.
result Demonstrates the model's effectiveness through various noise and intensity function scenarios.
Study shows how China's stock market reflects economic demand changes during COVID-19.
problem Understanding how stock market volatility is influenced by economic demand changes.
method Divided industries into demand-oriented groups and analyzed spillover networks.
result Spillover effects from demand-oriented sectors to consumption-oriented sectors increased during the outbreak.
New framework estimates demand responses across multiple contexts with limited price variation.
problem Estimating heterogeneous linear price-response functions across multiple contexts with limited price variation and confounding.
method Meta-learning framework that identifies conditional mean of task-specific causal demand parameters given a subset of task-specific observables.
result Improved recovery of demand responses relative to standard transfer-learning baselines.
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 …