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The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
A widespread belief in the blockchain security community is that automated techniques are only good for detecting shallow bugs, typically of small value. In this paper, we present the techniques and insights that have led us to repeatable…
Designing randomized online algorithms that perform reliably not only in expectation but also under unfavorable realizations of randomness is a fundamental challenge in online decision-making. In this paper, we study this challenge in…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
We study the out-of-sample properties of robust empirical optimization problems with smooth $\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness…
While $\mathcal{H}_\infty$ methods can introduce robustness against worst-case perturbations, their nominal performance under conventional stochastic disturbances is often drastically reduced. Though this fundamental tradeoff between…
This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall…
We analyze how uncertain technologies should be robustly regulated and how regulation should evolve with new information. An adaptive sandbox comprising a zero marginal tax up to an evolving quantity limit is (i) robust: it delivers optimal…
Smart contracts are Turing-complete programs that execute on the infrastructure of the blockchain, which often manage valuable digital assets. Solidity is one of the most popular programming languages for writing smart contracts on the…
The deepening penetration of renewable energy is challenging how power system operators cope with the associated variability and uncertainty in the unit commitment problem. Given its computational complexity, several optimization-based…
Advanced AI-Generated Content (AIGC) technologies have injected new impetus into teleoperation, further enhancing its security and efficiency. Edge AIGC networks have been introduced to meet the stringent low-latency requirements of…
Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…
The increase of renewables in the grid and the volatility of the load create uncertainties in the day-ahead prices of electricity markets. Adaptive robust optimization (ARO) and stochastic optimization have been used to make commitment and…
This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional uncertainty using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are…
We study the disequilibrium dynamics of a stylised model of production networks in which firms use perishable and non-substitutable intermediate inputs, so that adverse idiosyncratic productivity shocks can trigger downstream shortages and…
Data acquisition efficiency is a central challenge in deploying reinforcement learning in business and healthcare operations, where interactions are costly, slow, and often involve humans in the loop. This paper develops a unified large…
We solve a min-max problem in a robust exploratory mean-variance problem with drift uncertainty in this paper. It is verified that robust investors choose the Sharpe ratio with minimal $L^2$ norm in an admissible set. A reinforcement…
In online learning from non-stationary data streams, it is necessary to learn robustly to outliers and to adapt quickly to changes in the underlying data generating mechanism. In this paper, we refer to the former attribute of online…