Adhyyan Narang

Adhyyan Narang, Omid Sadeghi, Lillian J Ratliff et al. · uw

In the context of online interactive machine learning with combinatorial objectives, we extend purely submodular prior work to more general non-submodular objectives. This includes: (1) those that are additively decomposable into a sum of two terms (a monotone submodular and monotone supermodular term, known as a BP decomposition); and (2) those that are only weakly submodular. In both cases, this allows representing not only competitive (submodular) but also complementary (supermodular) relationships between objects, enhancing this setting to a broader range of applications (e.g., movie recommendations, medical treatments, etc.) where this is beneficial. In the two-term case, moreover, we study not only the more typical monolithic feedback approach but also a novel framework where feedback is available separately for each term. With real-world practicality and scalability in mind, we integrate Nystrom sketching techniques to significantly reduce the computational cost, including for the purely submodular case. In the Gaussian process contextual bandits setting, we show sub-linear theoretical regret bounds in all cases. We also empirically show good applicability to recommendation systems and data subset selection.

Marcus Williams, Micah Carroll, Adhyyan Narang et al. · berkeley

As LLMs become more widely deployed, there is increasing interest in directly optimizing for feedback from end users (e.g. thumbs up) in addition to feedback from paid annotators. However, training to maximize human feedback creates a perverse incentive structure for the AI to resort to manipulative or deceptive tactics to obtain positive feedback from users who are vulnerable to such strategies. We study this phenomenon by training LLMs with Reinforcement Learning with simulated user feedback in environments of practical LLM usage. In our settings, we find that: 1) Extreme forms of "feedback gaming" such as manipulation and deception are learned reliably; 2) Even if only 2% of users are vulnerable to manipulative strategies, LLMs learn to identify and target them while behaving appropriately with other users, making such behaviors harder to detect; 3) To mitigate this issue, it may seem promising to leverage continued safety training or LLM-as-judges during training to filter problematic outputs. Instead, we found that while such approaches help in some of our settings, they backfire in others, sometimes even leading to subtler manipulative behaviors. We hope our results can serve as a case study which highlights the risks of using gameable feedback sources -- such as user feedback -- as a target for RL.

Adhyyan Narang, Andrew Wagenmaker, Lillian Ratliff et al.

In this paper, we study the non-asymptotic sample complexity for the pure exploration problem in contextual bandits and tabular reinforcement learning (RL): identifying an epsilon-optimal policy from a set of policies with high probability. Existing work in bandits has shown that it is possible to identify the best policy by estimating only the difference between the behaviors of individual policies, which can be substantially cheaper than estimating the behavior of each policy directly. However, the best-known complexities in RL fail to take advantage of this and instead estimate the behavior of each policy directly. Does it suffice to estimate only the differences in the behaviors of policies in RL? We answer this question positively for contextual bandits but in the negative for tabular RL, showing a separation between contextual bandits and RL. However, inspired by this, we show that it almost suffices to estimate only the differences in RL: if we can estimate the behavior of a single reference policy, it suffices to only estimate how any other policy deviates from this reference policy. We develop an algorithm which instantiates this principle and obtains, to the best of our knowledge, the tightest known bound on the sample complexity of tabular RL.

Yue Sun, Adhyyan Narang, Halil Ibrahim Gulluk et al.

An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of the dataset is smaller than that of the model. While the prior literature focuses on the classical supervised setting, this paper aims to demystify overparameterization for meta-learning. Here we have a sequence of linear-regression tasks and we ask: (1) Given earlier tasks, what is the optimal linear representation of features for a new downstream task? and (2) How many samples do we need to build this representation? This work shows that surprisingly, overparameterization arises as a natural answer to these fundamental meta-learning questions. Specifically, for (1), we first show that learning the optimal representation coincides with the problem of designing a task-aware regularization to promote inductive bias. We leverage this inductive bias to explain how the downstream task actually benefits from overparameterization, in contrast to prior works on few-shot learning. For (2), we develop a theory to explain how feature covariance can implicitly help reduce the sample complexity well below the degrees of freedom and lead to small estimation error. We then integrate these findings to obtain an overall performance guarantee for our meta-learning algorithm. Numerical experiments on real and synthetic data verify our insights on overparameterized meta-learning.

Adhyyan Narang, Evan Faulkner, Dmitriy Drusvyatskiy et al.

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player performative prediction". We focus on two distinct solution concepts, namely (i) performatively stable equilibria and (ii) Nash equilibria of the game. The latter equilibria are arguably more informative, but can be found efficiently only when the game is monotone. We show that under mild assumptions, the performatively stable equilibria can be found efficiently by a variety of algorithms, including repeated retraining and the repeated (stochastic) gradient method. We then establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results.

Adhyyan Narang, Vidya Muthukumar, Anant Sahai

State-of-the-art deep learning classifiers are heavily overparameterized with respect to the amount of training examples and observed to generalize well on "clean" data, but be highly susceptible to infinitesmal adversarial perturbations. In this paper, we identify an overparameterized linear ensemble, that uses the "lifted" Fourier feature map, that demonstrates both of these behaviors. The input is one-dimensional, and the adversary is only allowed to perturb these inputs and not the non-linear features directly. We find that the learned model is susceptible to adversaries in an intermediate regime where classification generalizes but regression does not. Notably, the susceptibility arises despite the absence of model mis-specification or label noise, which are commonly cited reasons for adversarial-susceptibility. These results are extended theoretically to a random-Fourier-sum setup that exhibits double-descent behavior. In both feature-setups, the adversarial vulnerability arises because of a phenomenon we term spatial localization: the predictions of the learned model are markedly more sensitive in the vicinity of training points than elsewhere. This sensitivity is a consequence of feature lifting and is reminiscent of Gibb's and Runge's phenomena from signal processing and functional analysis. Despite the adversarial susceptibility, we find that classification with these features can be easier than the more commonly studied "independent feature" models.

Vidya Muthukumar, Adhyyan Narang, Vignesh Subramanian et al.

We compare classification and regression tasks in an overparameterized linear model with Gaussian features. On the one hand, we show that with sufficient overparameterization all training points are support vectors: solutions obtained by least-squares minimum-norm interpolation, typically used for regression, are identical to those produced by the hard-margin support vector machine (SVM) that minimizes the hinge loss, typically used for training classifiers. On the other hand, we show that there exist regimes where these interpolating solutions generalize well when evaluated by the 0-1 test loss function, but do not generalize if evaluated by the square loss function, i.e. they approach the null risk. Our results demonstrate the very different roles and properties of loss functions used at the training phase (optimization) and the testing phase (generalization).