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Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not known to hold generally with dependent samples, such as in online learning with time series data or distributed computing with Markovian training samples. In this paper, we show that SAA remains tractable when the distribution of unknown parameters is only observable through dependent instances and still enjoys asymptotic consistency and finite sample guarantees. Specifically, we provide a rigorous probability error analysis to derive 1 - beta confidence bounds for the out-of-sample performance of SAA estimators and show that these estimators are asymptotically consistent. We then, using monotone operator theory, study the performance of a class of stochastic first-order algorithms trained on a dependent source of data. We show that approximation error for these algorithms is bounded and concentrates around zero, and establish deviation bounds for iterates when the underlying stochastic process is phi-mixing. The algorithms presented can be used to handle numerically inconvenient loss functions such as the sum of a smooth and non-smooth function or of non-smooth functions with constraints. To illustrate the usefulness of our results, we present several stochastic versions of popular algorithms such as stochastic proximal gradient descent (S-PGD), stochastic relaxed Peaceman-Rachford splitting algorithms (S-rPRS), and numerical experiment.

AAAI 2022

Sample Average Approximation for Stochastic Optimization with Dependent Data: Performance Guarantees and Tractability

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

technical paper

Learning human driving behaviors is an efficient approach for self-driving vehicles. Traditional Imitation Learning (IL) methods assume that the expert demonstrations follow Markov Decision Processes (MDPs). However, in reality, this assumption does not always hold true. Spurious correlation may exist through the paths of historical variables because of the existence of unobserved confounders. Accounting for the latent causal relationships from unobserved variables to outcomes, this paper proposes Sequential Causal Imitation Learning (SeqCIL) for imitating driver behaviors. We develop a sequential causal template that generalizes the default MDP settings to one with Unobserved Confounders (MDPUC-HD). Then we develop a sufficient graphical criterion to determine when ignoring causality leads to poor performances in MDPUC-HD. Through the framework of Adversarial Imitation Learning, we develop a procedure to imitate the expert policy by blocking Ï€-backdoor paths at each time step. Our methods are evaluated on a synthetic dataset and a real-world highway driving dataset, both demonstrating that the proposed procedure significantly outperforms non-causal imitation learning methods.

Learning Human Driving Behaviors with Sequential Causal Imitation Learning

Clustering algorithms are often evaluated using metrics which compare with ground-truth cluster assignments, such as Rand index and NMI. Algorithm performance may vary widely for different hyperparameters, however, and thus model selection based on optimal performance for these metrics is discordant with how these algorithms are applied in practice, where labels are unavailable and tuning is often more art than science. It is therefore desirable to compare clustering algorithms not only on their optimally tuned performance, but also some notion of how realistic it would be to obtain this performance in practice. We propose an evaluation of clustering methods capturing this ease-of-tuning by modeling the expected best clustering score under a given computation budget. To encourage the adoption of the proposed metric alongside classic clustering evaluations, we provide an extensible benchmarking framework. We perform an extensive empirical evaluation of our proposed metric on popular clustering algorithms over a large collection of datasets from different domains, and observe that our new metric leads to several noteworthy observations.

An Evaluative Measure of Clustering Methods Incorporating Hyperparameter Sensitivity

Heterogeneous Graph Neural Networks (HGNNs) have drawn increasing attention in recent years and achieved outstanding performance in many tasks. However, despite their wide use, there is currently no understanding of their robustness to adversarial attacks. In this work, we first systematically study the robustness of HGNNs and show that they can be easily fooled by adding the adversarial edge between the target node and large-degree node (i.e., hub). Furthermore, we show two key reasons for such vulnerability of HGNNs: one is perturbation enlargement effect, i.e., HGNNs, failing to encode transiting probability, will enlarge the effect of the adversarial hub in comparison of GCNs, and the other is soft attention mechanism, i.e., such mechanism assigns positive attention values to obviously unreliable neighbors. Based on the two facts, we propose a novel robust HGNN framework RoHe against topology adversarial attacks by equipping an attention purifier, which can prune malicious neighbors based on topology and feature. Specifically, to eliminate the perturbation enlargement, we introduce the metapath-based transiting probability as the prior criterion of the purifier, restraining the confidence of malicious neighbors from the adversarial hub. Then the purifier learns to mask out neighbors with low confidence, thus can effectively alleviate the negative effect of malicious neighbors in the soft attention mechanism. Extensive experiments on different benchmark datasets for multiple HGNNs are conducted, where the considerable improvement of HGNNs under adversarial attacks will demonstrate the effectiveness and generalization ability of our defense framework.

Robust Heterogeneous Graph Neural Networks against Adversarial Attacks

Recent work has shown the potential benefit of  selective prediction systems that can learn to defer to a human when the predictions of the AI are unreliable, particularly to improve the reliability of AI systems in high-stakes applications like healthcare or conservation. However, most prior work assumes that human behavior remains unchanged when they solve a prediction task as part of a human-AI team as opposed to by themselves. We show that this is not the case by performing experiments to quantify human-AI interaction in the context of selective prediction. In particular, we study the impact of communicating different types of information to humans about the AI system's decision to defer. Using real-world conservation data and a selective prediction system that improves expected accuracy over that of the human or AI system working individually, we show that this messaging has a significant impact on the accuracy of human judgements. Our results study two components of the messaging strategy: 1) Whether humans are informed about the prediction of the AI system and 2) Whether they are informed about the decision of the selective prediction system to defer. By manipulating these messaging components, we show that it is possible to significantly boost human performance by informing the human of the decision to defer, but not revealing the  prediction of the AI. We therefore show that it is vital to consider how the decision to defer is communicated to a human when designing selective prediction systems, and that the composite accuracy of a human-AI team must be carefully evaluated using a human-in-the-loop framework.

Role of Human-AI Interaction in Selective Prediction

We model the societal task of redistricting political districts as a partitioning problem: Given a set of n points in the plane, each belonging to one of two parties, and a parameter k, our goal is to compute a partition P of the plane into regions so that each region contains roughly  s = n/k points. P should satisfy a notion of  "local" fairness, which is related to the notion of core, a well-studied concept in cooperative game theory. A region is associated with the majority party in that region, and a point is unhappy in P if it belongs to the minority party. A group D of roughly s contiguous points is called a deviating group with respect to P if majority of points in D are unhappy in P. The partition P is locally fair if there is no deviating group with respect to P.

This paper focuses on a restricted case when points lie in 1D. The problem is non-trivial even in this case. We consider both adversarial and "beyond worst-case" settings for this problem. For the former, we characterize the input parameters for which a locally fair partition always exists; we also show that a locally fair partition may not exist for certain parameters. We then consider input models where there are "runs" of red and blue points. For such clustered inputs, we show that a locally fair partition may not exist for certain values of s, but an approximate locally fair partition exists if we allow some regions to have smaller sizes. We finally present a polynomial-time algorithm for computing a locally fair partition if one exists.

Locally Fair Partitioning

This paper studies a function fitting problem which we coin  first-order convex fitting (FCF): given any two vector sequences x1, ..., xT and p1, ..., pT, when is it possible to  efficiently construct  a convex function f(x) that ``fits'' the two sequences in the first-order sense, i.e,   the (sub)gradient of f(xi) equals precisely pi, for all i = 1, ..., T? Despite a  basic question of convex analysis,  FCF has surprisingly been overlooked in the past literature. With an efficient constructive proof, we provide a clean answer to this question:  FCF   is possible  if and only if the two sequences are permutation stable: p1 * x1 + ... + pT * xT is greater than or equal to p1 * x'1 + ... + pT * x'T where x'1, ..., x'T is any permutation of x1, ..., xT.
 
We  demonstrate the usefulness of FCF in  two  applications. First, we study how it can be used as an empirical risk minimization procedure to learn the original convex function. We provide  efficient PAC-learnability bounds for special classes of convex functions  learned via FCF, and demonstrate its application to multiple economic problems where only function gradients (as opposed to function values)  can be observed. Second,  we empirically show how it can be used as a surrogate to significantly accelerate the minimization of the original convex function.

First-Order Convex Fitting and Its Application to Economics and Optimization

Strategy synthesis for multi-agent systems has proved to be a hard task, even when limited to two-player games with safety objectives. Generalized strategy synthesis, an extension of generalized planning which aims to produce a single solution for multiple (possibly infinitely many) planning instances, is a promising direction to deal with the state-space explosion problem. In this paper, we formalize the problem of generalized strategy synthesis in the situation calculus. The synthesis task involves second-order theorem proving generally. Thus we consider strategies aiming to maintain invariants; such strategies can be verified with first-order theorem proving. We propose a sound but incomplete approach to synthesize invariant strategies by adapting the framework of counterexample-guided refinement. The key idea for refinement is to generate a strategy using a model checker for a game constructed from the counterexample, and use it to refine the candidate general strategy. We implemented our method and did experiments with a number of game problems. Our system can successfully synthesize solutions for most of the domains within a reasonable amount of time.

Automated Synthesis of Generalized Invariant Strategies via Counterexample-Guided Strategy Refinement

Rotating savings and credit associations (roscas) are informal financial organizations common in settings where communities have reduced access to formal financial institutions. In a rosca, a fixed group of participants regularly contribute sums of money to a pot. This pot is then allocated periodically using lottery, aftermarket, or auction mechanisms. Roscas are empirically well-studied in economics. They are, however, challenging to study theoretically due to their dynamic nature. Typical economic analyses of roscas stop at coarse ordinal welfare comparisons to other credit allocation mechanisms, leaving much of roscas' ubiquity unexplained. In this work, we take an algorithmic perspective on the study of roscas. Building on techniques from the price of anarchy literature, we present worst-case welfare approximation guarantees. We further experimentally compare the welfare of outcomes as key features of the environment vary. These cardinal welfare analyses further rationalize the prevalence of roscas. We conclude by discussing several other promising avenues.

An Algorithmic Introduction to Savings Circles

Transformers achieve state-of-the-art performance for natural language processing tasks by pre-training on large-scale text corpora. They are extremely compute-intensive and have very high sample complexity. Memory replay is a mechanism that remembers and reuses past examples by saving to and replaying from a memory buffer. It has been successfully used in reinforcement learning and GANs due to better sample efficiency. In this paper, we propose Transformer with Memory Replay, which integrates memory replay with transformer, making transformer more sample efficient. Experiments on GLUE and SQuAD benchmark datasets showed that Transformer with Memory Replay can achieve at least 1% point increase compared to the baseline transformer model when pre-trained with the same number of examples. Further, by adopting a careful design that reduces the wall-clock time overhead of memory replay, we also empirically achieve a better runtime efficiency.

Transformer with Memory Replay

Question answering over semi-structured tables has attracted significant attention in the NLP community.
 However, most of the existing work focus on questions that can be answered with short-form answer, i.e. the answer is often a table cell or aggregation of multiple cells. 
 This can mismatch with the intents of users who want to ask more complex questions that require free-form answers such as explanations. 
 To bridge the gap, most recently, pre-trained sequence-to-sequence language models such as T5 are used for generating free-form answers based on the question and table inputs. 
 However, these pre-trained language models have weaker encoding abilities over table cells and schema. 
 To mitigate this issue, in this work, we present an intermediate pre-training framework, Generation-focused Table-based Intermediate Pre-training (GENTAP), that jointly learns representations of natural language questions and tables.
 GENTAP learns to generate via two training objectives to enhance the question understanding and table representation abilities for complex questions. 
 Based on experimental results, models that leverage GENTAP framework outperform the existing baselines on FETAQA benchmark. 
 The pre-trained models are not only useful for free-form question answering, but also for few-shot data-to-text generation task, thus showing good transfer ability by obtaining new state-of-the-art results.

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