Despite being an essential tool across engineering and finance, Monte Carlo simulation can be computationally intensive, especially in largescale, path-dependent problems that hinder straightforward parallelization. A natural alternative is to replace simulation with machine learning or surrogate prediction, though this introduces challenges in understanding the resulting errors. We introduce a Prediction-Enhanced Monte Carlo (PEMC) framework where we leverage machine learning prediction as control variates, thus maintaining unbiased evaluations instead of the direct use of ML predictors. Traditional control variate methods require knowledge of means and focus on per-sample variance reduction. In contrast, PEMC aims at overall cost-aware variance reduction, eliminating the need for mean knowledge. PEMC leverages pre-trained neural architectures to construct effective control variates and replaces computationally expensive sample-path generation with efficient neural network evaluations. This allows PEMC to address scenarios where no good control variates are known.

In this paper we establish a mathematically rigorous connection between Causal inference (C-inf) and the low-rank recovery (LRR). Using Random Duality Theory (RDT) concepts developed in [46,48,50] and novel mathematical strategies related to free probability theory, we obtain the exact explicit typical (and achievable) worst case phase transitions (PT). These PT precisely separate scenarios where causal inference via LRR is possible from those where it is not. We supplement our mathematical analysis with numerical experiments that confirm the theoretical predictions of PT phenomena, and further show that the two closely match for fairly small sample sizes. We obtain simple closed form representations for the resulting PTs, which highlight direct relations between the low rankness of the target C-inf matrix and the time of the treatment. Hence, our results can be used to determine the range of C-inf's typical applicability.

Causal inference (C-inf) deals with the design of estimation strategies that allow researchers to draw causal conclusions based on data. The overarching goal is to draw a conclusion regarding the effect of a causal variable, which is typically referred to as the "treatment" or the "intervention" on some outcome of interest. For example, suppose we want to estimate the causal effect of a drug on deadly cancer progression (vs no exposure to the drug). Then we want to compare metastasis in the patient's body one month after the drug regime has begun versus metastasis in the absence of exposure to the drug. The main challenge for causal inference is that we are not generally able to observe both of these states: at the point in time when we are measuring the outcomes, each individual either has had drug exposure or has not. The problem of estimating the counterfactual, i.e., what would have been the outcome in the absence of a treatement, is central in many disciplines, including economics, health, and social sciences (see, e.g.

Autonomous systems can substantially enhance a human's efficiency and effectiveness in complex environments. Machines, however, are often unable to observe the preferences of the humans that they serve. Despite the fact that the human's and machine's objectives are aligned, asymmetric information, along with heterogeneous sensitivities to risk by the human and machine, make their joint optimization process a game with strategic interactions. We propose a framework based on risk-sensitive dynamic games; the human seeks to optimize her risk-sensitive criterion according to her true preferences, while the machine seeks to adaptively learn the human's preferences and at the same time provide a good service to the human. We develop a class of performance measures for the proposed framework based on the concept of regret. We then evaluate their dependence on the risk-sensitivity and the degree of uncertainty. We present applications of our framework to self-driving taxis, and robo-financial advising.