Active learning enables us to reduce the annotation cost by adaptively selecting unlabeled instances to be labeled. For pool-based active learning, several effective methods with theoretical guarantees have been developed through maximizing some utility function satisfying adaptive submodularity. In contrast, there have been few methods for stream-based active learning based on adaptive submodularity. In this paper, we propose a new class of utility functions, policy-adaptive submodular functions, and prove this class includes many existing adaptive submodular functions appearing in real world problems. We provide a general framework based on policy-adaptive submodularity that makes it possible to convert existing pool-based methods to stream-based methods and give theoretical guarantees on their performance. In addition we empirically demonstrate their effectiveness comparing with existing heuristics on common benchmark datasets.

Active learning enables us to reduce the annotation cost by adaptively selecting unlabeled instances to be labeled. For pool-based active learning, several effective methods with theoretical guarantees have been developed through maximizing some utility function satisfying adaptive submodularity. In contrast, there have been few methods for stream-based active learning based on adaptive submodularity. In this paper, we propose a new class of utility functions, policy-adaptive submodular functions, and prove this class includes many existing adaptive submodular functions appearing in real world problems. We provide a general framework based on policy-adaptive submodularity that makes it possible to convert existing pool-based methods to stream-based methods and give theoretical guarantees on their performance. In addition we empirically demonstrate their effectiveness comparing with existing heuristics on common benchmark datasets.

Adaptive-submodularity is a widely used framework in stochastic optimization and machine learning [GK11, GK17, EKM21, ACN22]. Here, an algorithm makes sequential decisions while (partially) observing uncertainty. We study a basic problem in this context: covering an adaptive-submodular function at the minimum expected cost. We show that the natural greedy algorithm for this problem has approximation ratio at least 1.3 (1 + ln Q), where Q is the maximal function value. This is in contrast to special cases such as deterministic submodular cover or (independent) stochastic submodular cover, where the greedy algorithm achieves a tight (1 + ln Q) approximation ratio.

In this paper, we study the non-monotone adaptive submodular maximization problem subject to a cardinality constraint. We first revisit the adaptive random greedy algorithm proposed in \citep{gotovos2015non}, where they show that this algorithm achieves a $1/e$ approximation ratio if the objective function is adaptive submodular and pointwise submodular. It is not clear whether the same guarantee holds under adaptive submodularity (without resorting to pointwise submodularity) or not. Our first contribution is to show that the adaptive random greedy algorithm achieves a $1/e$ approximation ratio under adaptive submodularity. One limitation of the adaptive random greedy algorithm is that it requires $O(n\times k)$ value oracle queries, where $n$ is the size of the ground set and $k$ is the cardinality constraint. Our second contribution is to develop the first linear-time algorithm for the non-monotone adaptive submodular maximization problem. Our algorithm achieves a $1/e-\epsilon$ approximation ratio (this bound is improved to $1-1/e-\epsilon$ for monotone case), using only $O(n\epsilon^{-2}\log \epsilon^{-1})$ value oracle queries. Notably, $O(n\epsilon^{-2}\log \epsilon^{-1})$ is independent of the cardinality constraint. For the monotone case, we propose a faster algorithm that achieves a $1-1/e-\epsilon$ approximation ratio in expectation with $O(n \log \frac{1}{\epsilon})$ value oracle queries. We also generalize our study by considering a partition matroid constraint, and develop a linear-time algorithm for monotone and fully adaptive submodular functions.

Active learning enables us to reduce the annotation cost by adaptively selecting unlabeled instances to be labeled. For pool-based active learning, several effective methods with theoretical guarantees have been developed through maximizing some utility function satisfying adaptive submodularity. In contrast, there have been few methods for stream-based active learning based on adaptive submodularity. In this paper, we propose a new class of utility functions, policy-adaptive submodular functions, and prove this class includes many existing adaptive submodular functions appearing in real world problems. We provide a general framework based on policy-adaptive submodularity that makes it possible to convert existing pool-based methods to stream-based methods and give theoretical guarantees on their performance. In addition we empirically demonstrate their effectiveness comparing with existing heuristics on common benchmark datasets.

Adaptive sequential decision making is one of the central challenges in machine learning and artificial intelligence. In such problems, the goal is to design an interactive policy that plans for an action to take, from a finite set of n actions, given some partial observations. It has been shown that in many applications such as active learning, robotics, sequential experimental design, and active detection, the utility function satisfies adaptive submodularity, a notion that generalizes the notion of diminishing returns to policies. In this paper, we revisit the power of adaptivity in maximizing an adaptive monotone submodular function. We propose an efficient batch policy that with O(log n log k) adaptive rounds of observations can achieve an almost tight (1-1/e-ϵ) approximation guarantee with respect to an optimal policy that carries out k actions in a fully sequential setting.

Such problems are generally notoriously difficult. In this article, we review the recently discovered notion of adaptive submodularity, an intuitive diminishing returns condition that generalizes the classical notion of submodular set functions to sequential decision problems. Problems exhibiting the adaptive submodularity property can be efficiently and provably nearoptimally solved using simple myopic policies. We illustrate this concept in several case studies of interest in computational sustainability: First, we demonstrate how it can be used to efficiently plan for resolving uncertainty in adaptive management scenarios. Then, we show how it applies to dynamic conservation planning for protecting endangered species, a case study carried out in collaboration with the U.S. Geological Survey and the U.S. Fish and Wildlife Service.

Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse AI applications including management of sensing resources, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.

In this paper, we consider adaptive decision-making problems for stochastic state estimation with partial observations. First, we introduce the concept of weak adaptive submodularity, a generalization of adaptive submodularity, which has found great success in solving challenging adaptive state estimation problems. Then, for the problem of active diagnosis, i.e., discrete state estimation via active sensing, we show that an adaptive greedy policy has a near-optimal performance guarantee when the reward function possesses this property. We further show that the reward function for group-based active diagnosis, which arises in applications such as medical diagnosis and state estimation with persistent sensor faults, is also weakly adaptive submodular. Finally, in experiments of state estimation for an aircraft electrical system with persistent sensor faults, we observe that an adaptive greedy policy performs equally well as an exhaustive search.

Maximization of submodular functions has wide applications in artificial intelligence and machine learning. In this paper, we propose a scalable learning algorithm for maximizing an adaptive submodular function. The key structural assumption in our solution is that the state of each item is distributed according to a generalized linear model, which is conditioned on the feature vector of the item. Our objective is to learn the parameters of this model. We analyze the performance of our algorithm, and show that its regret is polylogarithmic in time and linear in the number of features. Finally, we evaluate our solution on two problems, preference elicitation and adaptive face detection, and demonstrate that high-quality policies can be learned sample efficiently.