There is a huge gap between the speeds of modern caches and main memories, and therefore cache misses account for a considerable loss of efficiency in programs. The predominant technique to address this issue has been Data Packing: data elements that are frequently accessed within time proximity are packed into the same cache block, thereby minimizing accesses to the main memory. We consider the algorithmic problem of Data Packing on a two-level memory system. Given a reference sequence R of accesses to data elements, the task is to partition the elements into cache blocks such that the number of cache misses on R is minimized. The problem is notoriously difficult: it is NP-hard even when the cache has size 1, and is hard to approximate for any cache size larger than 4. Therefore, all existing techniques for Data Packing are based on heuristics and lack theoretical guarantees. In this work, we present the first positive theoretical results for Data Packing, along with new and stronger negative results. We consider the problem under the lens of the underlying access hypergraphs, which are hypergraphs of affinities between the data elements, where the order of an access hypergraph corresponds to the size of the affinity group. We study the problem parameterized by the treewidth of access hypergraphs, which is a standard notion in graph theory to measure the closeness of a graph to a tree. Our main results are as follows: we show that there is a number q * depending on the cache parameters such that (a) if the access hypergraph of order q * has constant treewidth, then there is a linear-time algorithm for Data Packing; (b) the Data Packing problem remains NP-hard even if the access hypergraph of order q * −1 has constant treewidth. Thus, we establish a fine-grained dichotomy depending on a single parameter, namely, the highest order among access hypegraphs that have constant treewidth; and establish the optimal value q * of this parameter. Finally, we present an experimental evaluation of a prototype implementation of our algorithm. Our results demonstrate that, in practice, access hypergraphs of many commonly-used algorithms have small treewidth. We compare our approach with several state-of-the-art heuristic-based algorithms and show that our algorithm leads to significantly fewer cache-misses.

We consider the stochastic shortest path (SSP) problem for succinct Markov decision processes (MDPs), where the MDP consists of a set of variables, and a set of nondeterministic rules that update the variables. First, we show that several examples from the AI literature can be modeled as succinct MDPs. Then we present computational approaches for upper and lower bounds for the SSP problem: (a) for computing upper bounds, our method is polynomial-time in the implicit description of the MDP; (b) for lower bounds, we present a polynomial-time (in the size of the implicit description) reduction to quadratic programming. Our approach is applicable even to infinite-state MDPs. Finally, we present experimental results to demonstrate the effectiveness of our approach on several classical examples from the AI literature.

Multiple lines of evidence suggest that predictive models may benefit from algorithmic triage. Under algorithmic triage, a predictive model does not predict all instances but instead defers some of them to human experts. However, the interplay between the prediction accuracy of the model and the human experts under algorithmic triage is not well understood. In this work, we start by formally characterizing under which circumstances a predictive model may benefit from algorithmic triage. In doing so, we also demonstrate that models trained for full automation may be suboptimal under triage. Then, given any model and desired level of triage, we show that the optimal triage policy is a deterministic threshold rule in which triage decisions are derived deterministically by thresholding the difference between the model and human errors on a per-instance level. Building upon these results, we introduce a practical gradient-based algorithm that is guaranteed to find a sequence of triage policies and predictive models of increasing performance. Experiments on a wide variety of supervised learning tasks using synthetic and real data from two important applications-content moderation and scientific discovery-illustrate our theoretical results and show that the models and triage policies provided by our gradient-based algorithm outperform those provided by several competitive baselines.

Automated decision support systems promise to help human experts solve tasks more efficiently and accurately. However, existing systems typically require experts to understand when to cede agency to the system or when to exercise their own agency. Moreover, if the experts develop a misplaced trust in the system, their performance may worsen. In this work, we lift the above requirement and develop automated decision support systems that, by design, do not require experts to understand when to trust them to provably improve their performance. To this end, we focus on multiclass classification tasks and consider automated decision support systems that, for each data sample, use a classifier to recommend a subset of labels to a human expert. We first show that, by looking at the design of such systems from the perspective of conformal prediction, we can ensure that the probability that the recommended subset of labels contains the true label matches almost exactly a target probability value. Then, we identify the set of target probability values under which the human expert is provably better off predicting a label among those in the recommended subset and develop an efficient practical method to find a near-optimal target probability value. Experiments on synthetic and real data demonstrate that our system can help the experts make more accurate predictions and is robust to the accuracy of the classifier it relies on.

Most supervised learning models are trained for full automation. However, their predictions are sometimes worse than those by human experts on some specific instances. Motivated by this empirical observation, our goal is to design classifiers that are optimized to operate under different automation levels. More specifically, we focus on convex margin-based classifiers and first show that the problem is NP-hard. Then, we further show that, for support vector machines, the corresponding objective function can be expressed as the difference of two functions f = g - c, where g is monotone, non-negative and gamma-weakly submodular, and c is non-negative and modular. This representation allows a recently introduced deterministic greedy algorithm, as well as a more efficient randomized variant of the algorithm, to enjoy approximation guarantees at solving the problem. Experiments on synthetic and real-world data from several applications in medical diagnosis illustrate our theoretical findings and demonstrate that, under human assistance, supervised learning models trained to operate under different automation levels can outperform those trained for full automation as well as humans operating alone.