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Given a data set of size n in d&#39;-dimensional Euclidean space, the k-means problem asks for a set of k points (called centers) such that the sum of the l_2^2-distances between the data points and the set of centers is minimized. Previous work on this problem in the local differential privacy setting shows how to achieve multiplicative approximation factors arbitrarily close to optimal, but suffers high additive error. The additive error has also been seen to be an issue in implementations of differentially private k-means clustering algorithms in both the central and local settings. In this work, we introduce a new locally private k-means clustering algorithm that achieves near-optimal additive error whilst retaining constant multiplicative approximation factors and round complexity. Concretely, given any c&gt;âˆš2, our algorithm achieves O(k^(1 + O(1/(2c^2-1))) âˆš(d&#39; n) log d&#39; poly log n) additive error with an O(c^2) multiplicative approximation factor.

AAAI 2022

Locally Private $k$-Means Clustering with Constant Multiplicative Approximation and Near-Optimal Additive Error

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. 

AAAI 2021

Given a data set of size n in d'-dimensional Euclidean space, the k-means problem asks for a set of k points (called centers) such that the sum of the l_2^2-distances between the data points and the set of centers is minimized. Previous work on this problem in the local differential privacy setting shows how to achieve multiplicative approximation factors arbitrarily close to optimal, but suffers high additive error. The additive error has also been seen to be an issue in implementations of differentially private k-means clustering algorithms in both the central and local settings. In this work, we introduce a new locally private k-means clustering algorithm that achieves near-optimal additive error whilst retaining constant multiplicative approximation factors and round complexity. Concretely, given any c>âˆš2, our algorithm achieves O(k^(1 + O(1/(2c^2-1))) âˆš(d' n) log d' poly log n) additive error with an O(c^2) multiplicative approximation factor.

technical paper

The mathematical formalization of a neurological mechanism in the fruit-fly olfactory circuit as a locality sensitive hash (Flyhash) and bloom filter (FBF) has been recently proposed and "reprogrammed" for various learning tasks such as similarity search, outlier detection and text embeddings. We propose a novel reprogramming of this hash and bloom filter to emulate the canonical nearest neighbor classifier (NNC) in the challenging Federated Learning (FL) setup where training and test data are spread across parties and no data can leave their respective parties. Specifically, we utilize Flyhash and FBF to create the FlyNN classifier, and theoretically establish conditions where FlyNN matches NNC. We show how FlyNN is trained exactly in a FL setup with low communication overhead to produce FlyNNFL, and how it can be differentially private. Empirically, we demonstrate that (i) FlyNN matches NNC accuracy across 70 OpenML datasets, (ii) FlyNNFL training is highly scalable with low communication overhead, providing up to 8x speedup with 16 parties.

Federated Nearest Neighbor Classification with a Colony of Fruit-Flies

Optimal Transport (OT) has become a popular tool in machine learning to align finite datasets typically lying in the same vector space. To expand the range of possible applications, Co-Optimal Transport (Co-OT) jointly estimates two distinct transport plans, one for the rows (points) and one for the columns (features), to match two data matrices that might use different features. On the other hand, Gromov Wasserstein (GW) looks for a single transport plan from two pairwise intra-domain distance matrices. Both Co-OT and GW can be seen as specific extensions of OT to more complex data. In this paper, we propose a unified framework, called Optimal Tensor Transport (OTT), which takes the form of a generic formulation that encompasses OT, GW and Co-OT and can handle tensors of any order by learning possibly multiple transport plans. We derive theoretical results for the resulting new distance and present an efficient way for computing it. We further illustrate the interest of such a formulation in Domain Adaptation and Comparison-based Clustering.

Optimal Tensor Transport

Exploring unknown environments is a fundamental task in many domains, e.g., robot navigation, network security, and internet search. We initiate the study of a learning-augmented variant of the classical, notoriously hard online graph exploration problem by adding access to machine-learned predictions. We propose an algorithm that naturally integrates predictions into the well-known Nearest Neighbor (NN) algorithm and significantly outperforms any known online algorithm if the prediction is of high accuracy while maintaining good guarantees when the prediction is of poor quality. We provide theoretical worst-case bounds that gracefully degrade with the prediction error, and we complement them by computational experiments that confirm our results. Further, we extend our concept to a general framework to robustify algorithms. By interpolating carefully between a given algorithm and NN, we prove new performance bounds that leverage the individual good performance on particular inputs while establishing robustness to arbitrary inputs.

Robustification of Online Graph Exploration Methods

Advantage learning (AL) aims to improve the robustness of value-based reinforcement learning against estimation errors with action-gap-based regularization. Unfortunately, the method tends to be unstable in the case of function approximation. In this paper, we propose a simple variant of AL, named smoothing advantage learning (SAL), to alleviate this problem. The key to our method is to replace the original Bellman Optimal operator in AL with a smooth one so as to obtain more reliable estimation of the temporal difference target. We give a detailed account of the resulting action gap and the performance bound for approximate SAL. Further theoretical analysis reveals that the proposed value smoothing technique not only helps to stabilize the training procedure of AL by controlling the trade-off between convergence rate and the upper bound of the approximation errors, but is beneficial to increase the action gap between the optimal and sub-optimal action value as well.

Smoothing Advantage Learning

This paper considers the recently popular beyond-worst-case algorithm analysis model which integrates machine-learned predictions with online algorithm design. We consider the online Steiner tree problem in this model for both directed and undirected graphs. Steiner tree is known to have strong lower bounds in the online setting and any algorithm's worst-case guarantee is far from desirable.
 
 This paper considers algorithms that predict which terminal arrives online. The predictions may be incorrect and the algorithms' performance is parameterized by the number of incorrectly predicted terminals. These guarantees ensure that algorithms break through the online lower bounds with good predictions and the competitive ratio gracefully degrades as the prediction error grows. We then observe that the theory is predictive of what will occur empirically. We show on graphs where terminals are drawn from a distribution, the new online algorithms have strong performance even with modestly correct predictions.

Learning-Augmented Algorithms for Online Steiner Tree

Offline Reinforcement Learning (RL) aims at learning an optimal control from a fixed dataset, without interactions with the system. An agent in this setting should avoid selecting actions whose consequences cannot be predicted from the data. This is the converse of exploration in RL, which favors such actions. We thus take inspiration from the literature on bonus-based exploration to design a new offline RL agent. The core idea is to subtract a prediction-based exploration bonus from the reward, instead of adding it for exploration. This allows the policy to stay close to the support of the dataset and practically extends some previous pessimism-based offline RL methods to a deep learning setting with arbitrary bonuses. We also connect this approach to a more common regularization of the learned policy towards the data. Instantiated with a bonus based on the prediction error of a variational autoencoder, we show that our simple agent is competitive with the state of the art on a set of continuous control locomotion and manipulation tasks.

Offline Reinforcement Learning as Anti-Exploration

How much credit (or blame) should an action taken in a state get for a future reward? This is the fundamental temporal credit assignment problem in Reinforcement Learning (RL). One of the earliest and still most widely used heuristics is to assign this credit based on a scalar coefficient, lambda (treated as a hyperparameter), raised to the power of the time interval between the state-action and the reward. In this empirical paper, we explore heuristics based on more general pairwise weightings that are functions of the state in which the action was taken, the state at the time of the reward, as well as the time interval between the two. Of course it isn't clear what these pairwise weight functions should be, and because they are too complex to be treated as hyperparameters we develop a metagradient procedure for learning these weight functions during the usual RL training of a policy. Our empirical work shows that it is often possible to learn these pairwise weight functions during learning of the policy to achieve better performance than competing approaches.

Adaptive Pairwise Weights for Temporal Credit Assignment

Vision-based autonomous urban driving in dense traffic is quite challenging due to the complicated urban environment and the dynamics of the driving behaviors. Widely-applied methods either heavily rely on hand-crafted rules or learn from limited human experience, which makes them hard to generalize to rare but critical scenarios. In this paper, we present a novel CAscade Deep REinforcement learning framework, CADRE, to achieve model-free vision-based autonomous urban driving. In CADRE, to derive representative latent features from raw observations, we first offline train a Co-attention Perception Module (CoPM) that leverages the co-attention mechanism to learn the inter-relationships between the visual and control information from a pre-collected driving dataset. Cascaded by the frozen CoPM, we then present an efficient distributed proximal policy optimization framework to online learn the driving policy under the guidance of particularly designed reward functions. We perform a comprehensive empirical study with the CARLA NoCrash benchmark as well as specific obstacle avoidance scenarios in autonomous urban driving tasks. The experimental results well justify the effectiveness of CADRE and its superiority over the state-of-the-art by a wide margin.

CADRE: A Cascade Deep Reinforcement Learning Framework for Vision-Based Autonomous Urban Driving

Meta reinforcement learning (meta-RL) aims to learn a policy solving a set of training tasks simultaneously and quickly adapting to new tasks. It requires massive amounts of data drawn from training tasks to infer the common structure shared among tasks. Without heavy reward engineering, the sparse rewards in long-horizon tasks exacerbate the problem of sample efficiency in meta-RL. Another challenge in meta-RL is the discrepancy of difficulty level among tasks, which might cause one easy task dominating learning of the shared policy and thus preclude policy adaptation to new tasks. This work introduces a novel objective function to learn an action translator among training tasks. We theoretically verify that the value of the transferred policy with the action translator can be close to the value of the source policy and our objective function (approximately) upper bounds the value difference. We propose to combine the action translator with context-based meta-RL algorithms for better data collection and moreefficient exploration during meta-training. Our approach em-pirically improves the sample efficiency and performance ofmeta-RL algorithms on sparse-reward tasks.

Learning Action Translator for Meta Reinforcement Learning on Sparse-Reward Tasks

In addition to reproducing discriminatory relationships in the training data, machine learning (ML) systems can also introduce or amplify discriminatory effects. We refer to this as introduced unfairness, and investigate the conditions under which it may arise. To this end, we propose introduced total variation as a measure of introduced unfairness, and establish graphical conditions under which it may be incentivised to occur. These criteria imply that adding the sensitive attribute as a feature removes the incentive for introduced variation under well-behaved loss functions. Additionally, taking a causal perspective, introduced path-specific effects shed light on the issue of when specific paths should be considered fair.

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