Studying with Queried Hints – Google AI Weblog


In lots of computing purposes the system must make selections to serve requests that arrive in an internet trend. Take into account, as an example, the instance of a navigation app that responds to driver requests. In such settings there’s inherent uncertainty about essential elements of the issue. For instance, the preferences of the driving force with respect to options of the route are sometimes unknown and the delays of highway segments could be unsure. The sector of on-line machine studying research such settings and offers varied methods for decision-making issues beneath uncertainty.

A navigation engine has to determine route this consumer’s request. The satisfaction of the consumer will rely on the (unsure) congestion of the 2 routes and unknown preferences of the consumer on varied options, comparable to how scenic, secure, and many others., the route is.

A really well-known drawback on this framework is the multi-armed bandit drawback, during which the system has a set of n accessible choices (arms) from which it’s requested to decide on in every spherical (consumer request), e.g., a set of precomputed different routes in navigation. The consumer’s satisfaction is measured by a reward that relies on unknown elements comparable to consumer preferences and highway section delays. An algorithm’s efficiency over T rounds is in contrast towards the most effective fastened motion in hindsight via the remorse (the distinction between the reward of the most effective arm and the reward obtained by the algorithm over all T rounds). Within the consultants variant of the multi-armed bandit drawback, all rewards are noticed after every spherical and never simply the one performed by the algorithm.

An occasion of the consultants drawback. The desk presents the rewards obtained by following every of the three consultants at every spherical = 1, 2, 3, 4. The very best skilled in hindsight (and therefore the benchmark to check towards) is the center one, with complete reward 21. If, for instance, we had chosen skilled 1 within the first two rounds and skilled 3 within the final two rounds (recall that we have to choose earlier than observing the rewards of every spherical), we might have extracted reward 17, which might give a remorse equal to 21 – 17 = 4.

These issues have been extensively studied, and current algorithms can obtain sublinear remorse. For instance, within the multi-armed bandit drawback, the most effective current algorithms can obtain remorse that’s of the order √T. Nevertheless, these algorithms concentrate on optimizing for worst-case cases, and don’t account for the abundance of obtainable information in the actual world that enables us to coach machine discovered fashions able to aiding us in algorithm design.

In “On-line Studying and Bandits with Queried Hints” (introduced at ITCS 2023), we present how an ML mannequin that gives us with a weak trace can considerably enhance the efficiency of an algorithm in bandit-like settings. Many ML fashions are educated precisely utilizing related previous information. Within the routing utility, for instance, particular previous information can be utilized to estimate highway section delays and previous suggestions from drivers can be utilized to study the standard of sure routes. Fashions educated with such information can, in sure circumstances, give very correct suggestions. Nevertheless, our algorithms obtain sturdy ensures even when the suggestions from the mannequin is within the type of a much less express weak trace. Particularly, we merely ask that the mannequin predict which of two choices can be higher. Within the navigation utility that is equal to having the algorithm decide two routes and question an ETA mannequin for which of the 2 is quicker, or presenting the consumer with two routes with completely different traits and letting them decide the one that’s finest for them. By designing algorithms that leverage such a touch we are able to: Enhance the remorse of the bandits setting on an exponential scale when it comes to dependence on T and enhance the remorse of the consultants setting from order of √T to turn out to be impartial of T. Particularly, our higher sure solely relies on the variety of consultants n and is at most log(n).

Algorithmic Concepts

Our algorithm for the bandits setting makes use of the well-known higher confidence sure (UCB) algorithm. The UCB algorithm maintains, as a rating for every arm, the common reward noticed on that arm thus far and provides to it an optimism parameter that turns into smaller with the variety of instances the arm has been pulled, thus balancing between exploration and exploitation. Our algorithm applies the UCB scores on pairs of arms, primarily in an effort to make the most of the accessible pairwise comparability mannequin that may designate the higher of two arms. Every pair of arms i and j is grouped as a meta-arm (i, j) whose reward in every spherical is the same as the utmost reward between the 2 arms. Our algorithm observes the UCB scores of the meta-arms and picks the pair (i, j) that has the very best rating. The pair of arms are then handed as a question to the ML auxiliary pairwise prediction mannequin, which responds with the most effective of the 2 arms. This response is the arm that’s lastly utilized by the algorithm.

The choice drawback considers three candidate routes. Our algorithm as an alternative considers all pairs of the candidate routes. Suppose pair 2 is the one with the very best rating within the present spherical. The pair is given to the auxiliary ML pairwise prediction mannequin, which outputs whichever of the 2 routes is healthier within the present spherical.

Our algorithm for the consultants setting takes a follow-the-regularized-leader (FtRL) method, which maintains the full reward of every skilled and provides random noise to every, earlier than selecting the most effective for the present spherical. Our algorithm repeats this course of twice, drawing random noise two instances and selecting the very best reward skilled in every of the 2 iterations. The 2 chosen consultants are then used to question the auxiliary ML mannequin. The mannequin’s response for the most effective between the 2 consultants is the one performed by the algorithm.


Our algorithms make the most of the idea of weak hints to realize sturdy enhancements when it comes to theoretical ensures, together with an exponential enchancment within the dependence of remorse on the time horizon and even eradicating this dependence altogether. For instance how the algorithm can outperform current baseline options, we current a setting the place 1 of the n candidate arms is constantly marginally higher than the n-1 remaining arms. We evaluate our ML probing algorithm towards a baseline that makes use of the usual UCB algorithm to choose the 2 arms to undergo the pairwise comparability mannequin. We observe that the UCB baseline retains accumulating remorse whereas the probing algorithm shortly identifies the most effective arm and retains taking part in it, with out accumulating remorse.

An instance during which our algorithm outperforms a UCB primarily based baseline. The occasion considers n arms, one in every of which is all the time marginally higher than the remaining n-1.


On this work we discover how a easy pairwise comparability ML mannequin can present easy hints that show very highly effective in settings such because the consultants and bandits issues. In our paper we additional current how these concepts apply to extra complicated settings comparable to on-line linear and convex optimization. We imagine our mannequin of hints can have extra attention-grabbing purposes in ML and combinatorial optimization issues.


We thank our co-authors Aditya Bhaskara (College of Utah), Sungjin Im (College of California, Merced), and Kamesh Munagala (Duke College).


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