Related papers: Benefits of Monotonicity in Safe Exploration with …
We consider the problem of sequentially maximizing an unknown function $f$ over a set of actions of the form $(s,\mathbf{x})$, where the selected actions must satisfy a safety constraint with respect to an unknown safety function $g$. We…
Many applications require a learner to make sequential decisions given uncertainty regarding both the system's payoff function and safety constraints. In safety-critical systems, it is paramount that the learner's actions do not violate the…
In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f…
We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an a~priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on…
Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS…
Bayesian optimization based on the Gaussian process upper confidence bound (GP-UCB) offers a theoretical guarantee for optimizing black-box functions. In practice, however, black-box functions often involve input uncertainty. To handle such…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
Autonomous systems with machine learning-based perception can exhibit unpredictable behaviors that are difficult to quantify, let alone verify. Such behaviors are convenient to capture in probabilistic models, but probabilistic model…
Selecting the best alternative from a finite set represents a broad class of pure exploration problems. Traditional approaches to pure exploration have predominantly relied on Gaussian or sub-Gaussian assumptions on the performance…
In classical reinforcement learning, when exploring an environment, agents accept arbitrary short term loss for long term gain. This is infeasible for safety critical applications, such as robotics, where even a single unsafe action may…
Bandit algorithms have various application in safety-critical systems, where it is important to respect the system constraints that rely on the bandit's unknown parameters at every round. In this paper, we formulate a linear stochastic…
Exploration-exploitation of functions, that is learning and optimizing a mapping between inputs and expected outputs, is ubiquitous to many real world situations. These situations sometimes require us to avoid certain outcomes at all cost,…
Recently, there has been rising interest in Bayesian optimization -- the optimization of an unknown function with assumptions usually expressed by a Gaussian Process (GP) prior. We study an optimization strategy that directly uses an…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one…
This paper proposes a safe data-driven control framework for nonlinear systems with partially known dynamics. The method ensures stability and constraint satisfaction during online learning, assuming only a stabilizable linear approximation…
We propose a safe exploration algorithm for deterministic Markov Decision Processes with unknown transition models. Our algorithm guarantees safety by leveraging Lipschitz-continuity to ensure that no unsafe states are visited during…
Control barrier functions (CBFs) have recently introduced a systematic tool to ensure system safety by establishing set invariance. When combined with a nominal control strategy, they form a safety-critical control mechanism. However, the…
Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more…
In many real-world applications (e.g., planetary exploration, robot navigation), an autonomous agent must be able to explore a space with guaranteed safety. Most safe exploration algorithms in the field of reinforcement learning and…