Related papers: Bicausal Optimal Transport for Markov Chains via D…
We introduce a multivariate version of causal transport, which we name multicausal transport, involving several filtered processes among which causality constraints are imposed. Subsequently, we consider the barycenter problem for…
Suppose there are $n$ Markov chains and we need to pay a per-step \emph{price} to advance them. The "destination" states of the Markov chains contain rewards; however, we can only get rewards for a subset of them that satisfy a…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
We study optimal transport between probability measures supported on the same finite metric space, where the ground cost is a distance induced by a weighted connected graph. Building on recent work showing that the resulting Kantorovich…
In this paper we show that we can use Markov kernels as a model for optimal transport. This new framework can be easily translated into the standard coupling formulation of optimal transport, and we show that we can use a coupling as a…
Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized…
In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…
In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes…
Given a stochastic state process $(X_t)_t$ and a real-valued submartingale cost process $(S_t)_t$, we characterize optimal stopping times $\tau$ that minimize the expectation of $S_\tau$ while realizing given initial and target…
We investigate the design of pricing policies that enhance driver adherence to route guidance, ensuring effective routing control. The major novelty lies in that we adopt a Markov chain to model drivers' compliance rates conditioned on both…
We propose an optimal solution to a deterministic dynamic assignment problem by leveraging connections to the theory of discrete optimal transport to convert the combinatorial assignment problem into a tractable linear program. We seek to…
Platooning connected and autonomous vehicles (CAVs) provide significant benefits in terms of traffic efficiency and fuel economy. However, most existing platooning systems assume the availability of pre-determined plans, which is not…
The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a…
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…
Due to recurrent (e.g. daily or weekly) patterns and non-recurrent disruptions (e.g. caused by incidents), travel times in road networks are time-dependent and inherently random. This is challenging for travelers planning a future trip,…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…