Risk-averse learning with delayed feedback

summary

The gist

The gist In this paper, they investigate risk-averse learning using Conditional Value at Risk (CVaR) as a risk measure while incorporating feedback with random but bounded delays.

In short

The study investigates risk-averse learning using Conditional Value at Risk (CVaR) to manage potential losses when feedback is delayed randomly but within bounds. It develops two zeroth-order optimization algorithms: one-point and two-point, to estimate CVaR gradients. The two-point algorithm proves superior by achieving a smaller regret bound, making it more effective in real-world scenarios with time lags.

Key concepts

Conditional Value at Risk (CVaR): CVaR is a risk measure used to assess the potential tail risk of learning outcomes. It focuses on quantifying the expected loss beyond a certain high threshold. This approach helps in making decisions that are robust against worst-case scenarios, which is crucial in online learning where adverse events can occur.
Zeroth-Order Optimization: Since exact gradients for CVaR are often unavailable, this method estimates them by querying the objective function at slightly perturbed actions. This involves using a smoothed approximation of the CVaR function to derive an estimate of its gradient. It allows the algorithm to learn effectively even when analytical derivatives are too complex.
Dynamic Regret: Instead of static regret, dynamic regret is used to measure performance in environments where feedback arrives with delays. This metric accounts for the time-dependent nature of learning and incorporates the cumulative delay experienced by the system. It provides a more accurate measure of how well the algorithm adapts over time despite delayed observations.

Terminology used across episodes

Reinforcement Learning (RL) — explained in 25 episodes
Sample Complexity — explained in 20 episodes
Retrieval-Augmented Generation (RAG) — explained in 19 episodes
Flow Matching — explained in 18 episodes
Federated Learning — explained in 17 episodes
Quantum Fisher Information (QFI) — explained in 17 episodes

This episode discusses

The paper

Risk-averse learning with delayed feedback · Read on arXiv

Siyi Wang, Zifan Wang, Sandra Hirche, Karl H. Johansson

KTH Royal Institute of Technology · Technical University of Munich

In real-world scenarios, risk-averse learning is valuable for mitigating potential adverse outcomes. However, the delayed feedback makes it challenging to assess and manage risk effectively. In this paper, we investigate risk-averse learning using Conditional Value at Risk (CVaR) as risk measure, while incorporating feedback with random but bounded delays. We develop two risk-averse learning algorithms that rely on one-point and two-point zeroth-order optimization approaches, respectively. The dynamic regrets of the algorithms are analyzed in terms of the cumulative delay and the number of total samplings. In the absence of delay, the regret bounds match the established bounds of zeroth-order stochastic gradient methods for risk-averse learning. Furthermore, the two-point risk-averse learning outperforms the one-point algorithm by achieving a smaller regret bound. We provide numerical experiments on a dynamic pricing problem to demonstrate the performance of the algorithms.

Transcript

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: We're looking at the paper: "Risk-averse learning with delayed feedback".

Jane: The gist In this paper, they investigate risk-averse learning using Conditional Value at Risk (CVaR) as a risk measure while incorporating feedback with random but bounded delays.

Tom: First, who's behind it and why it matters.

Title and authors: Tom: Alright, so let's look at who wrote this. We have Siyi Wang, Zifan Wang, Sandra Hirche, and Karl H. Johansson as the authors of this paper on "Risk-averse learning with delayed feedback".

Jane: It’s interesting to see that it brings together folks from different fields—the IEEE fellows—to tackle a very practical problem in online learning where things are messy because of those time delays.

Lu: The focus here is really on how to design two specific risk-averse learning algorithms using zeroth-order optimization to handle this delayed feedback structure.

Meng: Zeroth-order optimization tells us that we can estimate the gradient of a complex function without needing its exact derivative, which is helpful when we don't have perfect access to the cost function itself.

Tom: So they build two versions: one-point risk-averse learning and a two-point risk-averse learning approach, which is what we need to see the comparison between.

Jane: That comparison is key because it shows how much better you can get at managing that uncertainty when dealing with those random delays.

Lalam: The title itself points to the core issue: making learning choices when the information arrives late and randomly.

The paper's summary: Tom: Okay, so what’s actually in this paper? It summarizes how they use CVaR as the risk measure and then develop these two algorithms based on zeroth-order optimization to estimate that gradient.

Jane: They specifically address the delay model where feedback arrives at a certain time slot, and they sort those losses by their generating time to build what they call a virtual timeline for analysis.

Lu: The authors quantify the error introduced by this delayed feedback by computing what they call cumulative delay, which is just the total amount of time that has passed without receiving the necessary feedback.

Meng: They are trying to get a firm estimate of how much regret we're going to incur over time, not just looking at a snapshot in time.

Tom: The main result they show is that both algorithms achieve sublinear regrets, which means as time T goes to infinity, the dynamic regret divided by T goes to zero.

Jane: That’s the fundamental goal: ensuring that even with these delays and risks, the algorithm doesn't just keep making terrible mistakes forever.

Lalam: They provide specific regret bounds for both versions based on terms like cumulative delay D and total samplings, which gives us a concrete way to measure performance.

The paper's improvements: Tom: Now, the paper suggests two main improvements over the existing one-point approach: they introduce a two-point risk-averse learning algorithm.

Jane: This second version uses two perturbed actions—one slightly larger and one slightly smaller—to query the cost function under both to estimate that CVaR gradient.

Lu: That difference between those two queries is what they use to estimate the CVaR gradient, which they call gbar nt, and it helps them get a tighter bound on regret.

Meng: The paper states that this two-point algorithm outperforms the one-point algorithm by achieving a smaller regret bound in terms of the dynamic regret DR2(T).

Tom: So, when you look at their theoretical results, for the one-point version, they get a bound that depends on T to the power of one minus a over four plus some terms involving D and p bar d p PT <ref:2409.16866#pg1>.

Jane: But for the two-point algorithm, they manage to achieve DR2(T) which is bounded by T to the power of one minus a over four plus something involving square roots and D <ref:2409.16866#pg1>.

Lalam: The key improvement in their analysis is showing that this two-point version provides better performance under delay conditions compared to the simpler one-point version.

Conclusion: Tom: So, wrapping up this "Risk-averse learning with delayed feedback" paper, both algorithms successfully achieve sublinear regrets, meaning they don't grow linearly with time.

Jane: And crucially, the two-point risk-averse learning algorithm is superior because it achieves a smaller regret bound than the one-point version under these delayed feedback conditions.

Lu: It also suggests that this second algorithm produces more consistent and stable outcomes in practice when things are delayed, even though the convergence speed might be different.

Meng: From a production standpoint, that stability is important; you want predictable performance even if your data stream is occasionally noisy with delays.

Lalam: So, to summarize, they used zeroth-order optimization to tackle CVaR gradients under delayed feedback and found the two-point method gives better regret bounds.

Tom: That’s it for this one. It shows that when you have delayed feedback, just having a basic risk-averse learner isn't enough; you need a method like Algorithm two for better results <ref:2409.16866#pg2>.

Jane: A very solid piece of work showing how to adapt existing optimization tools to handle the messy reality of real-world decision making with time lags.

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