Related papers: Distribution-free expectation operators for robust…

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We…

We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…

In this paper, we study a bivariate distributionally robust optimization problem with mean-covariance ambiguity set and half-space support. Under a conventional type of objective function widely adopted in inventory management, option…

We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…

Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…

We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this…

We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…

This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…

We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…

This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk…

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…

We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

We study deterministic monopoly pricing under partial knowledge of the market, where the seller has access only to summary statistics of the valuation distribution, such as the mean, dispersion, and maximum value. Using tools from…

We study a contest in which $N$ players sequentially draw from a distribution as many times as they want at a fixed cost per draw, with no recall, and the highest accepted value wins a prize. In the unique symmetric equilibrium, the…

When selling many goods with independent valuations, we develop a distributionally robust framework, consisting of a two-player game between seller and nature. The seller has only limited knowledge about the value distribution. The seller…

Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible…

Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…