Philippe Ciblat

Abdelghani Ghanem, Philippe Ciblat, Mounir Ghogho

Offline Reinforcement Learning (RL) is structured to derive policies from static trajectory data without requiring real-time environment interactions. Recent studies have shown the feasibility of framing offline RL as a sequence modeling task, where the sole aim is to predict actions based on prior context using the transformer architecture. However, the limitation of this single task learning approach is its potential to undermine the transformer model's attention mechanism, which should ideally allocate varying attention weights across different tokens in the input context for optimal prediction. To address this, we reformulate offline RL as a multi-objective optimization problem, where the prediction is extended to states and returns. We also highlight a potential flaw in the trajectory representation used for sequence modeling, which could generate inaccuracies when modeling the state and return distributions. This is due to the non-smoothness of the action distribution within the trajectory dictated by the behavioral policy. To mitigate this issue, we introduce action space regions to the trajectory representation. Our experiments on D4RL benchmark locomotion tasks reveal that our propositions allow for more effective utilization of the attention mechanism in the transformer model, resulting in performance that either matches or outperforms current state-of-the art methods.

Vincent Corlay, Joseph J. Boutros, Philippe Ciblat et al.

We characterize the complexity of the lattice decoding problem from a neural network perspective. The notion of Voronoi-reduced basis is introduced to restrict the space of solutions to a binary set. On the one hand, this problem is shown to be equivalent to computing a continuous piecewise linear (CPWL) function restricted to the fundamental parallelotope. On the other hand, it is known that any function computed by a ReLU feed-forward neural network is CPWL. As a result, we count the number of affine pieces in the CPWL decoding function to characterize the complexity of the decoding problem. It is exponential in the space dimension $n$, which induces shallow neural networks of exponential size. For structured lattices we show that folding, a technique equivalent to using a deep neural network, enables to reduce this complexity from exponential in $n$ to polynomial in $n$. Regarding unstructured MIMO lattices, in contrary to dense lattices many pieces in the CPWL decoding function can be neglected for quasi-optimal decoding on the Gaussian channel. This makes the decoding problem easier and it explains why shallow neural networks of reasonable size are more efficient with this category of lattices (in low to moderate dimensions).

Apostolos Avranas, Marios Kountouris, Philippe Ciblat

The problem of resource constrained scheduling in a dynamic and heterogeneous wireless setting is considered here. In our setup, the available limited bandwidth resources are allocated in order to serve randomly arriving service demands, which in turn belong to different classes in terms of payload data requirement, delay tolerance, and importance/priority. In addition to heterogeneous traffic, another major challenge stems from random service rates due to time-varying wireless communication channels. Various approaches for scheduling and resource allocation can be used, ranging from simple greedy heuristics and constrained optimization to combinatorics. Those methods are tailored to specific network or application configuration and are usually suboptimal. To this purpose, we resort to deep reinforcement learning (DRL) and propose a distributional Deep Deterministic Policy Gradient (DDPG) algorithm combined with Deep Sets to tackle the aforementioned problem. Furthermore, we present a novel way to use a Dueling Network, which leads to further performance improvement. Our proposed algorithm is tested on both synthetic and real data, showing consistent gains against state-of-the-art conventional methods from combinatorics, optimization, and scheduling metrics.

Hakim Hafidi, Mounir Ghogho, Philippe Ciblat et al.

We propose Graph Contrastive Learning (GraphCL), a general framework for learning node representations in a self supervised manner. GraphCL learns node embeddings by maximizing the similarity between the representations of two randomly perturbed versions of the intrinsic features and link structure of the same node's local subgraph. We use graph neural networks to produce two representations of the same node and leverage a contrastive learning loss to maximize agreement between them. In both transductive and inductive learning setups, we demonstrate that our approach significantly outperforms the state-of-the-art in unsupervised learning on a number of node classification benchmarks.

Vincent Corlay, Joseph J. Boutros, Philippe Ciblat et al.

We present new families of continuous piecewise linear (CPWL) functions in Rn having a number of affine pieces growing exponentially in $n$. We show that these functions can be seen as the high-dimensional generalization of the triangle wave function used by Telgarsky in 2016. We prove that they can be computed by ReLU networks with quadratic depth and linear width in the space dimension. We also investigate the approximation error of one of these functions by shallower networks and prove a separation result. The main difference between our functions and other constructions is their practical interest: they arise in the scope of channel coding. Hence, computing such functions amounts to performing a decoding operation.

Vincent Corlay, Joseph J. Boutros, Philippe Ciblat et al.

Point lattices and their decoding via neural networks are considered in this paper. Lattice decoding in Rn, known as the closest vector problem (CVP), becomes a classification problem in the fundamental parallelotope with a piecewise linear function defining the boundary. Theoretical results are obtained by studying root lattices. We show how the number of pieces in the boundary function reduces dramatically with folding, from exponential to linear. This translates into a two-layer ReLU network requiring a number of neurons growing exponentially in n to solve the CVP, whereas this complexity becomes polynomial in n for a deep ReLU network.

Vincent Corlay, Joseph J. Boutros, Philippe Ciblat et al.

A quasi-static flat multiple-antenna channel is considered. We show how real multilevel modulation symbols can be detected via deep neural networks. A multi-plateau sigmoid function is introduced. Then, after showing the DNN architecture for detection, we propose a twin-network neural structure. Batch size and training statistics for efficient learning are investigated. Near-Maximum-Likelihood performance with a relatively reasonable number of parameters is achieved.