I was not able to find why we should have a global innovation number for every new connection gene in NEAT.
From my little knowledge of NEAT, every innovation number corresponds directly with an node_in, node_out pair, so, why not only use this pair of ids instead of the innovation number? Which new information there is in this innovation number? chronology?
Update
Is it an algorithm optimization?
Note: this more of an extended comment than an answer.
You encountered a problem I also just encountered whilst developing a NEAT version for javascript. The original paper published in ~2002 is very unclear.
The original paper contains the following:
Whenever a new
gene appears (through structural mutation), a global innovation number is incremented
and assigned to that gene. The innovation numbers thus represent a chronology of the
appearance of every gene in the system. [..] ; innovation numbers are never changed. Thus, the historical origin of every
gene in the system is known throughout evolution.
But the paper is very unclear about the following case, say we have two ; 'identical' (same structure) networks:
The networks above were initial networks; the networks have the same innovation ID, namely [0, 1]. So now the networks randomly mutate an extra connection.
Boom! By chance, they mutated to the same new structure. However, the connection ID's are completely different, namely [0, 2, 3] for parent1 and [0, 4, 5] for parent2 as the ID is globally counted.
But the NEAT algorithm fails to determine that these structures are the same. When one of the parents scores higher than the other, it's not a problem. But when the parents have the same fitness, we have a problem.
Because the paper states:
In composing the offspring, genes are randomly chosen from veither parent at matching genes, whereas all excess or disjoint genes are always included from the more fit parent, or if they are equally fit, from both parents.
So if the parents are equally fit, the offspring will have connections [0, 2, 3, 4, 5]. Which means that some nodes have double connections... Removing global innovation counters, and just assign id's by looking at node_in and node_out, you avoid this problem.
So when you have equally fit parents, yes you have optimized the algorithm. But this is almost never the case.
Quite interesting: in the newer version of the paper, they actually removed that bolded line! Older version here.
By the way, you can solve this problem by instead of assigning innovation ID's, assign ID based on node_in and node_out using pairing functions. This creates quite interesting neural networks when fitness is equal:
I can't provide a detailed answer, but the innovation number enables certain functionality within the NEAT model to be optimal (like calculating the species of a gene), as well as allowing crossover between the variable length genomes. Crossover is not necessary in NEAT, but it can be done, due to the innovation number.
I got all my answers from here:
http://nn.cs.utexas.edu/downloads/papers/stanley.ec02.pdf
It's a good read
During crossover, we have to consider two genomes that share a connection between the two same nodes in their personal neural networks. How do we detect this collision without iterating both genome's connection genes over and over again for each step of crossover? Easy: if both connections being examined during crossover share an innovation number, they are connecting the same two nodes because they received that connection from the same common ancestor.
Easy Example:
If I am a genome with a specific connection gene with innovation number 'i', my children that take gene 'i' from me may eventually cross over with each other in 100 generations. We have to detect when these two evolved versions (alleles) of my gene 'i' are in collision to prevent taking both. Taking two of the same gene would cause the phenotype to probably loop and crash, killing the genotype.
When I created my first implementation of NEAT I thought the same... why would you keep a innovation number tracker...? and why would you use it only for one generation? Wouldn't be better to not keep it at all and use a key value par with the nodes connected?
Now that I am implementing my third revision I can see what Kenneth Stanley tried to do with them and why he wanted to keep them only for one generation.
When a connection is created, it will start its optimization in that moment. It marks its origin. If the same connection pops out in another generation, that will start its optimization then. Generation numbers try to separate the ones which come from a common ancestor, so the ones that have been optimized for many generations are not put side to side that one that was just generated. If a same connection is found in two genomes, that means that that gene comes from the same origin and thus, can be aligned.
Imagine then that you have your generation champion. Some of their genes will have 50 percent chance to be lost due that the aligned genes are treated equally.
What is better...? I haven't seen any experiments comparing the two approaches.
Kenneth Stanley also addressed this issue in the NEAT users page: https://www.cs.ucf.edu/~kstanley/neat.html
Should a record of innovations be kept around forever, or only for the current
generation?
In my implementation of NEAT, the record is only kept for a generation, but there
is nothing wrong with keeping them around forever. In fact, it may work better.
Here is the long explanation:
The reason I didn't keep the record around for the entire run in my
implementation of NEAT was because I felt that calling something the same
mutation that happened under completely different circumstances was not
intuitive. That is, it is likely that several generations down the line, the
"meaning" or contribution of the same connection relative to all the other
connections in a network is different than it would have been if it had appeared
generations ago. I used a single generation as a yardstick for this kind of
situation, although that is admittedly ad hoc.
That said, functionally speaking, I don't think there is anything wrong with
keeping innovations around forever. The main effect is to generate fewer species.
Conversely, not keeping them around leads to more species..some of them
representing the same thing but separated nonetheless. It is not currently clear
which method produces better results under what circumstances.
Note that as species diverge, calling a connection that appeared in one species a
different name than one that appeared earlier in another just increases the
incompatibility of the species. This doesn't change things much since they were
incompatible to begin with. On the other hand, if the same species adds a
connection that it added in an earlier generation, that must mean some members of
the species had not adopted that connection yet...so now it is likely that the
first "version" of that connection that starts being helpful will win out, and
the other will die away. The third case is where a connection has already been
generally adopted by a species. In that case, there can be no mutation creating
the same connection in that species since it is already taken. The main point is,
you don't really expect too many truly similar structures with different markings
to emerge, even with only keeping the record around for 1 generation.
Which way works best is a good question. If you have any interesting experimental
results on this question, please let me know.
My third revision will allow both options. I will add more information to this answer when I have results about it.
Related
I'm interested in replicating "hierachies" of data say similar to addresses.
Area
District
Sector
Unit
but you may have different pieces of data associated to each layer, so you may know the area of Sectors, but not of units, and you may know the population of a unit, basically its not a homogenious tree.
I know little about replication of data except brushing Brewers theorem/CAP, and some naive intuition about what eventual consistency is.
I'm looking for SIMPLE mechanisms to replicate this data from an ACID RDB, into other ACID RDBs, systemically the system needs to eventually converge, and obviously each RDB will enforce its own local consistent view, but any 2 nodes may not match at any given time (except 'eventually').
The simplest way to approach this is to simple store all the data in a single message from some designated leader and distribute it...like an overnight dump and load process, but thats too big.
So the next simplest thing (I thought) was if something inside an area changes, I can export the complete set of data inside an area, and load it into the nodes, thats still quite a coarse algorithm.
The next step was if, say an 'object' at any level changed, was to send all the data in the path to that 'object', i.e. if something in a sector is amended, you would send the data associated to the sector, its parent the district, and its parent the sector (with some sort of version stamp and lets say last update wins)....what i wanted to do was to ensure that any replication 'update' was guaranteed to succeed (so it needs the whole path, which potentially would be created if it didn't exist).
then i stumbled on CRDTs and thought....ah...I'm reinventing the wheel here, and the algorithms are allegedly easy in principle, but tricky to get correct in practice
are there standards accepted patterns to do this sort of thing?
In my use case the hierarchies are quite shallow, and there is only a single designated leader (at this time), I'm quite attracted to state based CRDTs because then I can ignore ordering.
Simplicity is the key requirement.
Actually it appears I've reinvented (in a very crude naive way) the SHELF algorithm.
I'll write some code and see if I can get it to work, and try to understand whats going on.
This question is related to my previous question
Is it possible to get a legit range info when using a SMT constraint with Z3
So it seems that "efficiently" finding the maximum range info is not proper, given typical 32-bit vectors and so on. But on the other hand, I am thinking whether it is feasible to find certain "sub-maximum" range info, which hopefully becomes more efficient. Another thing is that we may want to have certain "safe" guarantee, say for all elements in the sub-maximum range, they must satisfy the constraint, but there could exist some other solutions that would satisfy the constraint as well.
I am currently exploring whether model counting technique could make sense in this setting. Any thoughts would be appreciated very much. Thanks.
General case
This is not just a question of efficiency. Consider a problem where you have two variables a and b, and a single constraint:
a != b
What's the range of b? (maximum or otherwise?)
You can say all values are legitimate. But that would be wrong, as obviously the choice of a impacts the choice of b. The more variables you have around, the more complicated the problem will become. I don't think the problem is even well defined in this case, so searching for a solution (efficient or otherwise) doesn't make much sense.
Single variable assumption
Having said that, I think you can come up with a solution if you assume there's precisely one variable in the system. (Or, alternatively, if you fix all the other variables to some predefined constants.) If you're willing to go down this path, then you can implement a binary search algorithm to find a reasonably sized range by simply proving the quantified formula
Exists([b], And(b >= minBound, b <= maxBound, Not(constraints)))
Once you get unsat for this, you have your range. So long as you get sat, you can adjust your minBound/maxBound to search within smaller ranges. In the worst case, this can turn into a linear walk, but you can "cut-down" this search by making sure you go down a significant size in each step. That could be a parameter to the whole search, depending on how large you want your intervals to be. It'll have to be a choice between trying to find a maximal range, and how long you want to spend in this search. Of course, if you cut-down too much, you can miss a big interval, but that's the cost of efficiency.
Example1 (Good case) There's a single constraint that says b != 5. Then your search will be quick and depending on which branch you'll go, you'll either find [0, 4] or [6, 255] assuming 8-bit words.
Example2 (Bad case) There's a single constraint that says b is even. Then your search will exhibit worst-case behavior, and if your "cut-down" size is 1, you'll possibly iterate 255 times before you settle down on [0, 0]; assuming z3 gives you the maximum odd number in each call.
I hope that illustrates the point. In general, though, I'd assume you'd be closer to the "good case" for practical applications and even if your cut-down size is minimal you can most likely converge in a few iterations. Of course, this entirely depends on your problem domain, but I'd expect it to hold for software analysis in general.
How do people deal with problems where the legal actions in different states are different? In my case I have about 10 actions total, the legal actions are not overlapping, meaning that in certain states, the same 3 states are always legal, and those states are never legal in other types of states.
I'm also interested in see if the solutions would be different if the legal actions were overlapping.
For Q learning (where my network gives me the values for state/action pairs), I was thinking maybe I could just be careful about which Q value to choose when I'm constructing the target value. (ie instead of choosing the max, I choose the max among legal actions...)
For Policy-Gradient type of methods I'm less sure of what the appropriate setup is. Is it okay to just mask the output layer when computing the loss?
There are two closely related works in recent two years:
[1] Boutilier, Craig, et al. "Planning and learning with stochastic action sets." arXiv preprint arXiv:1805.02363 (2018).
[2] Chandak, Yash, et al. "Reinforcement Learning When All Actions Are Not Always Available." AAAI. 2020.
Currently this problem seems to not have one, universal and straight-forward answer. Maybe because it is not that of an issue?
Your suggestion of choosing the best Q value for legal actions is actually one of the proposed ways to handle this. For policy gradients methods you can achieve similar result by masking the illegal actions and properly scaling up the probabilities of the other actions.
Other approach would be giving negative rewards for choosing an illegal action - or ignoring the choice and not making any change in the environment, returning the same reward as before. For one of my personal experiences (Q Learning method) I've chosen the latter and the agent learned what he has to learn, but he was using the illegal actions as a 'no action' action from time to time. It wasn't really a problem for me, but negative rewards would probably eliminate this behaviour.
As you see, these solutions don't change or differ when the actions are 'overlapping'.
Answering what you've asked in the comments - I don't believe you can train the agent in described conditions without him learning the legal/illegal actions rules. This would need, for example, something like separate networks for each set of legal actions and doesn't sound like the best idea (especially if there are lots of possible legal action sets).
But is the learning of these rules hard?
You have to answer some questions yourself - is the condition, that makes the action illegal, hard to express/articulate? It is, of course, environment-specific, but I would say that it is not that hard to express most of the time and agents just learn them during training. If it is hard, does your environment provide enough information about the state?
Not sure if I understand your question correctly, but if you mean that in certain states some actions are impossible then you simply reflect it in the reward function (big negative value). You can even decide to end the episode if it is not clear what state would the illegal action result in. The agent should then learn that those actions are not desirable in the specific states.
In exploration mode, the agent might still choose to take the illegal actions. However, in exploitation mode it should avoid them.
I recently built a DDQ agent for connect-four and had to address this. Whenever a column was chosen that was already full with tokens, I set the reward equivalent to losing the game. This was -100 in my case and it worked well.
In connect four, allowing an illegal move (effectively skipping a turn) can in some cases be advantageous for the player. This is why I set the reward equivalent to losing and not a smaller negative number.
So if you set the negative reward greater than losing, you'll have to consider in your domain what are the implications of allowing illegal moves to happen in exploration.
I have process parameter data from semiconductor manufacturing.and requirement is to suggest what could be the best parameter adjustment to be made to process parameter to get better yield ie best path for high yield. what machine learning /Statistical models best suits this requirement
Note:I have thought of using decision tree which can give us best path for high yield.
Would like to know it any other methods that can be more efficient
data is like
lotno x1 x2 x3 x4 x5 yield(%)
<95% yield is considered as 0 and >95% as 1
I'm not really sure of the question here, but as a former semiconductor process engineer, here is how I look at the yield improvement approach - perspective.
Process Development.
DOE: Typically, I would run structured DOEs to understand my process (#4). I would first identify "potential" 'factors', and run various "screening" experiments to identify statistical significance. With the goal basically here to identify the most statistically significant (and for that matter, least significant) factors. So these are inherently simple experiments, low # of "levels" which don't target understanding of the curvature of the response surface, they just look for magnitude change of response vs factor. Generally, I am most concerned with 'Process' factors, but it is important to recognize that the influence of variable inputs can come from more than just "machine knobs' as example. Variable can arise from 1) People, 2) Environment (moisture, temp, etc), 3) consumables (used in the process), 4) Equipment (is 40 psi on this tool really 40 psi and the same as 40 psi on a different tool) 4) Process variable settings.
With the most statistically significant factors, I would run more elaborate DOE using the major factors and analyze this data to develop a model. There are generally more 'levels' used here to allow for curvature insight of the response surface via the analysis. There are many types of well known standard experimental design structures here. And there is software such as JMP that is specifically set up to do this analysis.
From here, the idea would be to generate a model in the form of Response = F (Factors). That allows you to essentially optimize the response based upon these factors where the response is a reflection of your yield criteria.
From here, the engineer would typically execute confirmation runs with optimized factors to confirm optimized response.
Note that the software analysis typically allows for the engineer to illuminate any run order dependence. The execution of the DOE is typically performed in a randomized cell fashion. (Each 'cell' is a set of conditions for the experiment). Similarly the experiments include some level of repetition to gauge 'repeatability' of the 'system'. This inclusion can be explicit (run the same cell twice), but there is also some level of repeatability inherent in the design as well since you are running multiple cells, albeit at difference settings. But generally, the experiment includes explicitly repeated cells.
And finally there is the concept of manufacturability, which includes constraints of time, cost, physical limits, equipment capability, etc. (The ideal process works great, but it takes 10 years, costs 1 million dollars and requires projected settings outsides the capability of the tool.)
Since you have manufacturing data, hopefully, you have the data that captures the other types of factors as well (1,2,3), so you should specifically analyze the data to try to identify such effects. This is typically done as A vs B comparisons. Person A vs B, Tool A vs B, Consumable A vs B, Consumable lot A vs B, Summer vs Winter, etc.
Basically, there are all sorts of comparisons you could envision here and check for statistically differences across two sets of populations.
A comment on response: What is the yield criteria? You should know this in order to formulate the model. For semiconductors, we have both line yield (process yield) but there is also device yield. I assume for your work, you are primarily concerned with line yield. So minimizing variability in the factors (from 1,2,3,4) to achieve the desired response (target response(s) with minimal variability) is the primary goal.
APC (Advanced Process Control).
In many cases, there is significant trending that results from whatever reason; crappy tool control (the tool heats up), crappy consumable (the target material wears, the polishing pad wears, the chemical bath gets loaded, whatever), and so the idea here is how to adjust the next batch/lot/wafer based upon the history of what came prior. Either improve the manufacturing to avoid/minimize this trending (run order dependence) or adjust process to accommodate it to achieve the desired response.
Time for lunch, hope this helps...if you post on the specific process module type, and even equipment and consumables, I might be able to provide more insight.
I just got an interview question.
"Assume you want to build a statistical or machine learning model, but you have very limited data on hand. Your boss told you can duplicate original data several times, to make more data for building the model" Does it help?
Intuitively, it does not help, because duplicating original data doesn't create more "information" to feed the model.
But is there anyone can explain it more statistically? Thanks
Consider e.g. variance. The data set with the duplicated data will have the exact same variance - you don't have a more precise estimate of the distrbution afterwards.
There are, however, some exceptions. For example bootstrap validation helps when evaluating your model, but you have very little data.
Well, it depends on exactly what one means by "duplicating the data".
If one is exactly duplicating the whole data set a number of times, then methods based on maximum likelihood (as with many models in common use) must find exactly the same result since the log likelihood function of the duplicated data is exactly a multiple of the unduplicated data's log likelihood, and therefore has the same maxima. (This argument doesn't apply to methods which aren't based on the likelihood function; I believe that CART and other tree models, and SVM's, are such models. In that case you'll have to work out a different argument.)
However, if by duplicating, one means duplicating the positive examples in a classification problem (which is common enough, since there are often many more negative examples than positive), then that does make a difference, since the likelihood function is modified.
Also if one means bootstrapping, then that, too, makes a difference.
PS. Probably you'll get more interest in this question on stats.stackexchange.com.