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Monotonic Partially Observable Markov Decision Processes (POMDPs), where the system state progressively decreases until a restorative action is performed, can be used to model sequential repair problems effectively. This paper considers the…

Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

In Oncology, trials evaluating drug combinations are becoming more common. While combination therapies bring the potential for greater efficacy, they also create unique challenges for ensuring drug safety. In Phase-I dose escalation trials…

Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…

We examine nonparametric dose-finding designs that use toxicity estimates based on all available data at each dose allocation decision. We prove that one such design family, called here "interval design", converges almost surely to the…

Policies for Partially Observable Markov Decision Processes (POMDPs) are often designed using a nominal system model. In practice, this model can deviate from the true system during deployment due to factors such as calibration drift or…

We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown…

Dose-escalation trials in oncology drug development still today typically aim to identify 1-size-fits-all dose recommendations, as arbitrary quantiles of the toxicity thresholds evident in patient samples. In the late 1990s efforts to…

In real-world reinforcement learning (RL) scenarios, agents often encounter partial observability, where incomplete or noisy information obscures the true state of the environment. Partially Observable Markov Decision Processes (POMDPs) are…

Partially Observable Markov Decision Processes (POMDPs) are a natural and general model in reinforcement learning that take into account the agent's uncertainty about its current state. In the literature on POMDPs, it is customary to assume…

Structures and properties of many inorganic compounds have been collected historically. However, it only covers a very small portion of possible inorganic crystals, which implies the presence of numerous currently unknown compounds. A…

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…

In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where…

Paired cluster-randomized experiments (pCRTs) are common across many disciplines because there is often natural clustering of individuals, and paired randomization can help balance baseline covariates to improve experimental precision.…

Cohort-based enrollment can slow down dose-finding trials since the outcomes of the previous cohort must be fully evaluated before the next cohort can be enrolled. This results in frequent suspension of patient enrollment. The issue is…

The traditional more-is-better dose selection paradigm, developed based on cytotoxic chemotherapeutics, is often problematic When applied to the development of novel molecularly targeted agents (e.g., kinase inhibitors, monoclonal…

In this study, we consider the subset selection problems with submodular or monotone discrete objective functions under partition matroid constraints where the thresholds are dynamic. We focus on POMC, a simple Pareto optimization approach…

There are multiple cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at that time point. Identifying…

Contemporary continual learning approaches typically select prompts from a pool, which function as supplementary inputs to a pre-trained model. However, this strategy is hindered by the inherent noise of its selection approach when handling…