Lê Nguyên Hoang

Sadegh Farhadkhani, Rachid Guerraoui, Nirupam Gupta et al.

Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been proposed to enhance the robustness of D-SGD to such machines, previous works either resort to strong assumptions (trusted server, homogeneous data, specific noise model) or impose a gradient computational cost that is several orders of magnitude higher than that of D-SGD. We present MoNNA, a new algorithm that (a) is provably robust under standard assumptions and (b) has a gradient computation overhead that is linear in the fraction of faulty machines, which is conjectured to be tight. Essentially, MoNNA uses Polyak's momentum of local gradients for local updates and nearest-neighbor averaging (NNA) for global mixing, respectively. While MoNNA is rather simple to implement, its analysis has been more challenging and relies on two key elements that may be of independent interest. Specifically, we introduce the mixing criterion of $(α, λ)$-reduction to analyze the non-linear mixing of non-faulty machines, and present a way to control the tension between the momentum and the model drifts. We validate our theory by experiments on image classification and make our code available at https://github.com/LPD-EPFL/robust-collaborative-learning.

Lê Nguyên Hoang

This paper proposes a careful separation between an entity's epistemic system and their decision system. Crucially, Bayesian counterfactuals are estimated by the epistemic system; not by the decision system. Based on this remark, I prove the existence of Newcomb-like problems for which an epistemic system necessarily expects the entity to make a counterfactually bad decision. I then address (a slight generalization of) Newcomb's paradox. I solve the specific case where the player believes that the predictor applies Bayes rule with a supset of all the data available to the player. I prove that the counterfactual optimality of the 1-Box strategy depends on the player's prior on the predictor's additional data. If these additional data are not expected to reduce sufficiently the predictor's uncertainty on the player's decision, then the player's epistemic system will counterfactually prefer to 2-Box. But if the predictor's data is believed to make them quasi-omniscient, then 1-Box will be counterfactually preferred. Implications of the analysis are then discussed. More generally, I argue that, to better understand or design an entity, it is useful to clearly separate the entity's epistemic, decision, but also data collection, reward and maintenance systems, whether the entity is human, algorithmic or institutional.

El-Mahdi El-Mhamdi, Sadegh Farhadkhani, Rachid Guerraoui et al.

We study Byzantine collaborative learning, where $n$ nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and $f < n$ nodes can behave arbitrarily. We prove that collaborative learning is equivalent to a new form of agreement, which we call averaging agreement. In this problem, nodes start each with an initial vector and seek to approximately agree on a common vector, which is close to the average of honest nodes' initial vectors. We present two asynchronous solutions to averaging agreement, each we prove optimal according to some dimension. The first, based on the minimum-diameter averaging, requires $ n \geq 6f+1$, but achieves asymptotically the best-possible averaging constant up to a multiplicative constant. The second, based on reliable broadcast and coordinate-wise trimmed mean, achieves optimal Byzantine resilience, i.e., $n \geq 3f+1$. Each of these algorithms induces an optimal Byzantine collaborative learning protocol. In particular, our equivalence yields new impossibility theorems on what any collaborative learning algorithm can achieve in adversarial and heterogeneous environments.

El-Mahdi El-Mhamdi, Rachid Guerraoui, Arsany Guirguis et al.

Machine Learning (ML) solutions are nowadays distributed, according to the so-called server/worker architecture. One server holds the model parameters while several workers train the model. Clearly, such architecture is prone to various types of component failures, which can be all encompassed within the spectrum of a Byzantine behavior. Several approaches have been proposed recently to tolerate Byzantine workers. Yet all require trusting a central parameter server. We initiate in this paper the study of the ``general'' Byzantine-resilient distributed machine learning problem where no individual component is trusted. We show that this problem can be solved in an asynchronous system, despite the presence of $\frac{1}{3}$ Byzantine parameter servers and $\frac{1}{3}$ Byzantine workers (which is optimal). We present a new algorithm, ByzSGD, which solves the general Byzantine-resilient distributed machine learning problem by relying on three major schemes. The first, Scatter/Gather, is a communication scheme whose goal is to bound the maximum drift among models on correct servers. The second, Distributed Median Contraction (DMC), leverages the geometric properties of the median in high dimensional spaces to bring parameters within the correct servers back close to each other, ensuring learning convergence. The third, Minimum-Diameter Averaging (MDA), is a statistically-robust gradient aggregation rule whose goal is to tolerate Byzantine workers. MDA requires loose bound on the variance of non-Byzantine gradient estimates, compared to existing alternatives (e.g., Krum). Interestingly, ByzSGD ensures Byzantine resilience without adding communication rounds (on a normal path), compared to vanilla non-Byzantine alternatives. ByzSGD requires, however, a larger number of messages which, we show, can be reduced if we assume synchrony.

Lê Nguyên Hoang

This paper discussed the {\it robust alignment} problem, that is, the problem of aligning the goals of algorithms with human preferences. It presented a general roadmap to tackle this issue. Interestingly, this roadmap identifies 5 critical steps, as well as many relevant aspects of these 5 steps. In other words, we have presented a large number of hopefully more tractable subproblems that readers are highly encouraged to tackle. Hopefully, this combination allows to better highlight the most pressing problems, how every expertise can be best used to, and how combining the solutions to subproblems might add up to solve robust alignment.

El Mahdi El Mhamdi, Rachid Guerraoui, Lê Nguyên Hoang et al.

We address the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analytically in the case of two populations, with a uniform bonus-malus on the zones where each population is a majority. We then address the general case of n populations, where the entanglement of populations does not allow a similar analytical solution. We show that an approximate solution with an arbitrarily high level of precision can be computed with linear programming. Finally, we address the inverse problem where the error should not go beyond a certain value and we seek to minimize the discrimination.

Lê Nguyên Hoang, Rachid Guerraoui

Deep learning relies on a very specific kind of neural networks: those superposing several neural layers. In the last few years, deep learning achieved major breakthroughs in many tasks such as image analysis, speech recognition, natural language processing, and so on. Yet, there is no theoretical explanation of this success. In particular, it is not clear why the deeper the network, the better it actually performs. We argue that the explanation is intimately connected to a key feature of the data collected from our surrounding universe to feed the machine learning algorithms: large non-parallelizable logical depth. Roughly speaking, we conjecture that the shortest computational descriptions of the universe are algorithms with inherently large computation times, even when a large number of computers are available for parallelization. Interestingly, this conjecture, combined with the folklore conjecture in theoretical computer science that $ P \neq NC$, explains the success of deep learning.