The actor losses used in DoubleGum, SAC, and DDPG are all derived from the same principle. SAC (Haarnoja et al., 2018a,b) has a policy with learned variance and state-independent Section B.1 shows this for the actor losses of DoubleGum, SAC, and DDPG. We now relate the critic losses to each other, starting from the most general case, DoubleGum. The SAC noise model is derived from Equation 16 in three ways. In continuous control, Fujimoto et al. (2018) introduced Twin Networks, a method that improved Follow-up work selects a quantile estimate from an ensemble (Kuznetsov et al., 2020; Chen et al., 2021; Ball et al., 2023), which we demonstrate is Moskovitz et al. (2021) and Ball et al. (2023) showed that the appropriate Garg et al. (2023) present a method of estimating its value using Gumbel regression.

Probabilities of causation provide principled ways to assess causal relationships but face computational challenges due to partial identifiability and latent confounding. This paper introduces both algorithmic simplifications, significantly reducing the computational complexity of calculating tighter bounds for these probabilities, and a novel methodological framework for Root Cause Analysis that systematically employs these causal metrics to rank entire causal paths.

Selection bias, arising from the systematic inclusion or exclusion of certain samples, poses a significant challenge to the validity of causal inference. While Bareinboim et al. introduced methods for recovering unbiased observational and interventional distributions from biased data using partial external information, the complexity of the backdoor adjustment and the method's strong reliance on observational data limit its applicability in many practical settings. In this paper, we formally discover the recoverability of $P(Y^*_{x^*})$ under selection bias with experimental data. By explicitly constructing counterfactual worlds via Structural Causal Models (SCMs), we analyze how selection mechanisms in the observational world propagate to the counterfactual domain. We derive a complete set of graphical and theoretical criteria to determine that the experimental distribution remain unaffected by selection bias. Furthermore, we propose principled methods for leveraging partially unbiased observational data to recover $P(Y^*_{x^*})$ from biased experimental datasets. Simulation studies replicating realistic research scenarios demonstrate the practical utility of our approach, offering concrete guidance for mitigating selection bias in applied causal inference.

Task offloading management in 6G vehicular networks is crucial for maintaining network efficiency, particularly as vehicles generate substantial data. Integrating secure communication through authentication introduces additional computational and communication overhead, significantly impacting offloading efficiency and latency. This paper presents a unified framework incorporating lightweight Identity-Based Cryptographic (IBC) authentication into task offloading within cloud-based 6G Vehicular Twin Networks (VTNs). Utilizing Proximal Policy Optimization (PPO) in Deep Reinforcement Learning (DRL), our approach optimizes authenticated offloading decisions to minimize latency and enhance resource allocation. Performance evaluation under varying network sizes, task sizes, and data rates reveals that IBC authentication can reduce offloading efficiency by up to 50% due to the added overhead. Besides, increasing network size and task size can further reduce offloading efficiency by up to 91.7%. As a countermeasure, increasing the transmission data rate can improve the offloading performance by as much as 63%, even in the presence of authentication overhead. The code for the simulations and experiments detailed in this paper is available on GitHub for further reference and reproducibility [1].

This paper presents an interesting and valuable contribution to the small but growing literature on fairness in machine learning. Specifically, it provides at least three contributions: (1) a definition of counter factual fairness; (2) an algorithm for learning a model under counter factual fairness; and (3) experiments with that algorithm. The value of the contributions of the current paper is sufficient for acceptance, though significant improvements could be made in the clarity of exposition of the algorithm and the extent of the experimentation with the algorithm. Section 4.2 outlines why is is likely that very strong assumptions will need to be made to effectively estimate a model of Y under counterfactual fairness. The assumptions (and the implied analysis techniques) suggest conclusions that will not be particularly robust to violations of those assumptions.

Leveraging the development of structural causal model (SCM), researchers can establish graphical models for exploring the causal mechanisms behind machine learning techniques. As the complexity of machine learning applications rises, single-world interventionism causal analysis encounters theoretical adaptation limitations. Accordingly, cross-world counterfactual approach extends our understanding of causality beyond observed data, enabling hypothetical reasoning about alternative scenarios. However, the joint involvement of cross-world variables, encompassing counterfactual variables and real-world variables, challenges the construction of the graphical model. Twin network is a subtle attempt, establishing a symbiotic relationship, to bridge the gap between graphical modeling and the introduction of counterfactuals albeit with room for improvement in generalization. In this regard, we demonstrate the theoretical breakdowns of twin networks in certain cross-world counterfactual scenarios. To this end, we propose a novel teleporter theory to establish a general and simple graphical representation of counterfactuals, which provides criteria for determining teleporter variables to connect multiple worlds. In theoretical application, we determine that introducing the proposed teleporter theory can directly obtain the conditional independence between counterfactual variables and real-world variables from the cross-world SCM without requiring complex algebraic derivations. Accordingly, we can further identify counterfactual causal effects through cross-world symbolic derivation. We demonstrate the generality of the teleporter theory to the practical application. Adhering to the proposed theory, we build a plug-and-play module, and the effectiveness of which are substantiated by experiments on benchmarks.

We study the computational complexity of counterfactual reasoning in relation to the complexity of associational and interventional reasoning on structural causal models (SCMs). We show that counterfactual reasoning is no harder than associational or interventional reasoning on fully specified SCMs in the context of two computational frameworks. The first framework is based on the notion of treewidth and includes the classical variable elimination and jointree algorithms. The second framework is based on the more recent and refined notion of causal treewidth which is directed towards models with functional dependencies such as SCMs. Our results are constructive and based on bounding the (causal) treewidth of twin networks -- used in standard counterfactual reasoning that contemplates two worlds, real and imaginary -- to the (causal) treewidth of the underlying SCM structure. In particular, we show that the latter (causal) treewidth is no more than twice the former plus one. Hence, if associational or interventional reasoning is tractable on a fully specified SCM then counterfactual reasoning is tractable too. We extend our results to general counterfactual reasoning that requires contemplating more than two worlds and discuss applications of our results to counterfactual reasoning with a partially specified SCM that is coupled with data. We finally present empirical results that measure the gap between the complexities of counterfactual reasoning and associational/interventional reasoning on random SCMs.

Brian Huge and I just posted a working paper following six months of research and development on function approximation by artificial intelligence (AI) in Danske Bank. One major finding was that training machine learning (ML) models for regression (i.e. Given those differential labels, we can write simple, yet unreasonably effective training algorithms, capable of learning accurate function approximations with remarkable speed and accuracy from small datasets, in a stable manner, without the need of additional regularization or optimization of hyperparameters, e.g. by cross-validation. In this post, we briefly summarize these algorithms under the name differential machine learning, highlighting the main intuitions and benefits and commenting TensorFlow implementation code. All the details are found in the working paper, the online appendices and the Colab notebooks.

There has been much recent work using machine learning to answer causal queries. Most focus on interventional queries, such as the conditional average treatment effect. However, as noted by Pearl, interventional queries only form part of a larger hierarchy of causal queries, with counterfactuals sitting at the top. Despite this, our community has not fully succeeded in adapting machine learning tools to answer counterfactual queries. This work addresses this challenge by showing how to implement twin network counterfactual inference -- an alternative to abduction, action, & prediction counterfactual inference -- with deep learning to estimate counterfactual queries. We show how the graphical nature of twin networks makes them particularly amenable to deep learning, yielding simple neural network architectures that, when trained, are capable of counterfactual inference. Importantly, we show how to enforce known identifiability constraints during training, ensuring the answer to each counterfactual query is uniquely determined. We demonstrate our approach by using it to accurately estimate the probabilities of causation -- important counterfactual queries that quantify the degree to which one event was a necessary or sufficient cause of another -- on both synthetic and real data.