Diversification Quotients: Quantifying Diversification via Risk Measures

To overcome several limitations of existing diversification indices, we introduce the diversification quotient (DQ). Defined through a parametric family of risk measures, DQ satisfies three natural properties, namely, non-negativity, location invariance and scale invariance, which are shown to be conflicting for any traditional diversification index based on a single risk measure. We pay special attention to the two most important classes of risk measures in banking and insurance, the Value-at-Risk (VaR) and the Expected Shortfall (ES, also called CVaR). DQs based on VaR and ES enjoy many convenient technical properties, and they are efficient to optimize in portfolio selection. By analyzing the popular multivariate models of elliptical and regular varying distributions, we find that DQ can properly capture tail heaviness and common shocks which are neglected by traditional diversification indices. When illustrated with financial data, DQ is intuitive to interpret, and its performance is competitive when contrasted with other diversification methods in portfolio optimization

ODE-based Recurrent Model-free Reinforcement Learning for POMDPs

Neural ordinary differential equations (ODEs) are widely recognized as the standard for modeling physical mechanisms, which help to perform approximate inference in unknown physical or biological environments. In partially observable (PO) environments, how to infer unseen information from raw observations puzzled the agents. By using a recurrent policy with a compact context, context-based reinforcement learning provides a flexible way to extract unobservable information from historical transitions. To help the agent extract more dynamics-related information, we present a novel ODE-based recurrent model combines with model-free reinforcement learning (RL) framework to solve partially observable Markov decision processes (POMDPs). We experimentally demonstrate the efficacy of our methods across various PO continuous control and meta-RL tasks. Furthermore, our experiments illustrate that our method is robust against irregular observations, owing to the ability of ODEs to model irregularly-sampled time series.Comment: Accepted by NeurIPS 202

Understanding the Difficulty of Training Transformers

Transformers have proved effective in many NLP tasks. However, their training requires non-trivial efforts regarding designing cutting-edge optimizers and learning rate schedulers carefully (e.g., conventional SGD fails to train Transformers effectively). Our objective here is to understand $\textit{what complicates Transformer training}$ from both empirical and theoretical perspectives. Our analysis reveals that unbalanced gradients are not the root cause of the instability of training. Instead, we identify an amplification effect that influences training substantially -- for each layer in a multi-layer Transformer model, heavy dependency on its residual branch makes training unstable, since it amplifies small parameter perturbations (e.g., parameter updates) and results in significant disturbances in the model output. Yet we observe that a light dependency limits the model potential and leads to inferior trained models. Inspired by our analysis, we propose Admin ($\textbf{Ad}$aptive $\textbf{m}$odel $\textbf{in}$itialization) to stabilize stabilize the early stage's training and unleash its full potential in the late stage. Extensive experiments show that Admin is more stable, converges faster, and leads to better performance. Implementations are released at: https://github.com/LiyuanLucasLiu/Transforemr-Clinic.Comment: EMNLP 202