Planner Metrics Should Satisfy Independence of Irrelevant Alternatives (Position Paper)
Abstract
We argue that planner evaluation metrics should satisfy the independence of irrelevant alternatives criterion, i.e., the decision whether planner A is ranked higher or lower than plan- ner B should be independent of planner
C. We show that three metrics used in classical planning competitions do not neces- sarily satisfy this criterion and highlight alternative metrics that do so.
Introduction
Arrow’s impossibility theorem is an important result from social choice theory (Arrow 1950).
One of the fairness criteria it suggests is independence of irrelevant alternatives (IIA).
In the setting of planning competitions, IIA translates to the requirement that the decision whether planner A is ranked higher or lower than planner B must depend only on the performance of planners A and B and not on another planner C.
We believe that IIA is a critical requirement for planner evaluation metrics.
In the following, we show three planner evaluation metrics that do not satisfy IIA and give alternative metrics that do satisfy it.
IPC Sequential Satisﬁcing Track
In the satisﬁcing track of the International Planning Competition (IPC) planners are given 30 minutes to ﬁnd plans.
The time for ﬁnding plans is ignored, but cheaper plans are preferred.
More precisely, the track uses the following metric (which we call sat ) to evaluate a planner P on task π : P gets a score of 0 if it fails to solve π within the resource limits and a score of Cost ∗ / Cost if it solves π , where Cost is the cost of the cheapest plan that P ﬁnds for π and Cost ∗ is the cost of a reference plan, i.e., a cheapest known plan for π .
The total score for a planner is the sum of its scores over all tasks.
Itis easy to see that sat satisﬁes IIA if Cost ∗ is always the cost of an optimal plan for π .
However, if we take solutions for π found by the competing planners into account when computing Cost ∗ ( π ) , sat does not satisfy IIA anymore.
We show this claim with the small example in Table 1.
The leftmost table shows the cost of the reference plan R and the cost of the plans that planners A , B and C ﬁnd for [Table] two tasks π 1 and π 2 .
If only A and B participate in the competition, A achieves a higher sat score than B (middle table).
However, if C enters the competition as well, B is ranked higher than A (rightmost table).
To mitigate this problem, it is important to use domainspeciﬁc solvers to ﬁnd reference plans of high quality.
IPC Agile Track
IPC 2014 introduced the agile track (Vallati, Chrpa, and McCluskey 2014).
It ignores solution costs and evaluates planners solely by how fast they are able to ﬁnd a solution.
The ﬁrst agile competition used the following evaluation metric, which we call agl 2014 : for each task π in the benchmark set that a planner P solves in under ﬁve minutes, P gets a score of 1 / (1 + log 10 ( T/T ∗ )) , where T is the time P needs for solving π and T ∗ is the minimum runtime of any participating planner.
As in the satisﬁcing track, the total score for a planner is the sum of its scores over all tasks.
Clearly, agl 2014 does not satisfy IIA, which is the reason the agile track used a different evaluation metric in 2018.
The 2018 metric, which we call agl 2018 , evaluates each planner on its own.
If T is the time in seconds a planner P needs to solve task π , 1 P gets the score agl 2018 ( P , π ) , which is deﬁned as
[Equation]
It is easy to see that agl 2018 indeed satisﬁes IIA and is therefore preferable to agl 2014 in our opinion.
Sparkle Planning Challenge
In 2019, the Sparkle Planning Challenge will be held for the ﬁrst time.
Its “primary goal [...] is to analyse the contribution of each planner to the real state of the art”.
Consequently, the challenge measures the marginal contribution of each participating planner to a portfolio selector, i.e., an algorithm that chooses a single planner from the set of all participating planners online for a given task.
In essence, the
Sparkle evaluation metric, which we call sparkle , evaluates a planner P by the penalized average runtime the portfolio selector achieves when it can select from all competing planners except P .
The following example shows that sparkle does not satify IIA.
Assume planners A and B enter the Sparkle Planning Challenge.
Planner A solves a single task in 200 seconds while planner B solves 100 tasks and never uses more than a second.
Clearly, B wins the competition.
Now imagine that planner C also participates in the challenge.
Planner
C solves the same tasks as B and has almost the same runtimes.
Under sparkle , B and C contribute almost nothing to the portfolio (since without B the selector can still choose C and vice versa) and planner A wins the challenge.
We believe there is no reason for penalizing planners B and C for performing similarly.
In fact, we consider sparkle to be quite problematic, since a scenario similar to the one in the example above is quite likely to come up in competitions and we see mainly two reasons for why it might.
First, the evaluation metric is easily gameable.
If a team wants to win the challenge, it just needs to guess which other planners might be participating and submit similar planners in addition to the “real” planner.
By the competition rules, a team of three can submit one real planner and 6 “fake” planners.
Having the leader board available online before the submission deadline and the IPC 2018 planners readily available makes the metric easy to exploit.
Second, and we think this reason is even more important than the ﬁrst one, the evaluation metric penalizes collaboration.
It favors developing closed-source planning systems over developing planning systems openly and allowing others to build on the system.
This is the case, since all planners that share the same base planning system are likely to perform well on similar tasks and therefore receive low marginal contribution scores.
Openly developed planning systems have a disadvantage in the IPC as well.
However, under IPC metrics a planner that builds on an open planning system might score slightly higher than the system, but under the Sparkle Challenge metric both would get a very low score.
An evaluation metric that satisﬁes IIA does not suffer from these problems.
In order to let sparkle satisfy IIA, we only need to change it slightly.
Instead of evaluating a planner with respect to all participating planners, we can evaluate it with respect to a ﬁxed set of baseline planners.
We believe that this set of baseline planners should be accumulated over time.
A reasonable ﬁrst set of baseline planners could be the set of all planners from the last IPC agile track. Subsequent challenges should add planners from later agile tracks and/or Sparkle planning challenges. In our opinion, the competition rules for the Sparkle Planning Challenge have another drawback: they discourage submitting multiple planners.
A team that submits a single planner is likely to receive a higher score for this planner if they do not submit another planner.
To encourage teams to submit multiple planners, we think that for each task π , participants should get the maximum score any of their planners achieves for π .
This way, teams that advance the state of the art with multiple approaches are awarded for all ideas.
Acknowledgments
We thank the anonymous reviewers for their helpful comments.