I've noticed that there is a limit to how fast one of my box2d bodies can move (2 meters per tick), is there a way I could increase this cap?
You can use World.setVelocityThreshold(1000000.0f); to increase the the limit, but this can lead to other problems.
A better alternative is to reduce the size of the world, so the limit of 2 meters per calculation step is sufficient.
This answer describes the problems when increasing the velocity threshold and describes other possible solutions to this kind of problem.
Related
I am trying to train a neural network to classify words into different categories.
I notice two things:
When I use a smaller batch_size (like 8,16,32) the loss is not decreasing, but rather sporadically varying. When I use a larger batch_size (like 128, 256), the loss is going going down, but very slowly.
More importantly, when I use a larger EPOCH value, my model does a good job at reducing the loss. However I'm using a really large value (EPOCHS = 10000).
Question:
How to get the optimal EPOCH and batch_size values?
There is no way to decide on these values based on some rules. Unfortunately, the best choices depend on the problem and the task. However, I can give you some insights.
When you train a network, you calculate a gradient which would reduce the loss. In order to do that, you need to backpropagate the loss. Now, ideally, you compute the loss based on all of the samples in your data because then you consider basically every sample and you come up with a gradient that would capture all of your samples. In practice, this is not possible due to the computational complexity of calculating gradient on all samples. Because for every update, you have to compute forward-pass for all your samples. That case would be batch_size = N, where N is the total number of data points you have.
Therefore, we use small batch_size as an approximation! The idea is instead of considering all the samples, we say I compute the gradient based on some small set of samples but the thing is I am losing information regarding the gradient.
Rule of thumb:
Smaller batch sizes give noise gradients but they converge faster because per epoch you have more updates. If your batch size is 1 you will have N updates per epoch. If it is N, you will only have 1 update per epoch. On the other hand, larger batch sizes give a more informative gradient but they convergence slower.
That is the reason why for smaller batch sizes, you observe varying losses because the gradient is noisy. And for larger batch sizes, your gradient is informative but you need a lot of epochs since you update less frequently.
The ideal batch size should be the one that gives you informative gradients but also small enough so that you can train the network efficiently. You can only find it by trying actually.
I am having trouble with understanding deep learning.
I see that deep learning is basically about inductive process, and so the function must be adjusted enough until it hits the right target.
But I can not figure out how much those w and b values should be changed in each trials. Is there any rule for the adjustment?
If there is not, then is there any trick? like, some formulas those are normally used.
And, do more networks always perform better?
I understand that single layer can not hit as many target as multiple layer does, but I don't know if 3-layer is better than 2-layer.
The changes of w and b are based on the gradient of them.
You can calculate the gradient by taking derivative from the error (depending on the loss function). As you decrease the gradient, the error also decreases.
The maximum change of your gradient is gradient/gradient_magnitude * total_error/gradient_magnitude.
When you increase or decrease your function by its unit gradient, the output will be increased or decreased about the magnitude of its gradient. For that reason, the maximum changes of w and b are gradient*err/mag^2.
However, changing gradients to their limits is not recommended because problem of local minimum could occur. Therefore, learning rate or dropout algorithms are usually implemented.
The method above is not the only way to adjust the factors. Genetic algorithm, RBM, or reinforced learning methods could be implemented to replace or help above method.
I am trying to come up with an efficient way to characterize two narrowband tones separated by about 900kHz (one at around 100kHZ and one at around 1MHz once translated to baseband). They don't move much in freq over time but may have amplitude variations we want to monitor.
Each tone is roughly about 100Hz wide and we are required to characterize these two beasts over long periods of time down to a resolution of about 0.1 Hz. The samples are coming in at over 2M Samples/sec (TBD) to adequately acquire the highest tone.
I'm trying to avoid (if possible) doing brute force >2MSample FFTs on the data once a second to extract frequency domain data. Is there an efficient approach? Something akin to performing two (much) smaller FFTs around the bands of interest? Ive looked at Goertzel and chirp z methods but I am not certain it helps save processing.
Something akin to performing two (much) smaller FFTs around the bands of interest
There is, it's called Goertzel, and is kind of the FFT for single bins, and you already have looked at it. It will save you CPU time.
Anyway, there's no reason to do a 2M-point FFT; first of all, you only want a resolution of about 1/20 the sampling rate, hence, a 20-point FFT would totally do, and should be pretty doable for your CPU at these low rates; since you don't seem to care about phase of your tones, FFT->complex_to_mag.
However, there's one thing that you should always do: look at your signal of interest, and decimate down to the rate that fits exactly that. Since GNU Radio's filters are implemented cleverly, the filter itself will only run at the decimated rate, and you can spend the CPU cycles saved on a better filter.
Because a direct decimation from 2MHz to 100Hz (decimation: 20000) will really have an ugly filter length, you should do this multi-rated:
I'd try first decimating by 100, and then in a second step by 100, leaving you with 200Hz observable spectrum. The xlating fir filter blocks will let you use a simple low-pass filter (use the "Low-Pass Filter Taps" block to define a variable that contains such taps) as a band-selector.
I need to program a solver for the game of Peg solitaire / Senku
There's already a question here but the proposed answer is a brute force algorithm with backtracking, which is not the solution I'm looking for.
I need to find some heuristic to apply an A* algorithm. The remaining pegs is not a good heuristic as every move discards one peg so the cost is always uniform.
Any ideas?
I was reading a paper talking about this problem link,
and they propose 3 heuristics:
1 - The number of nodes are available for the next step, considering which more available next's steps, better the node.
2 - Number of isolated peg's - as few isolated peg's better the node.
3 - Less peg's in the board better the node.
This may be not the better heuristics for this problem, but seems to be a simple approach.
You can do as rossum suggested. Another option would be to use the sum of distances (or some other function of the distances) from the center. Or you could combine the two.
Here's the background... in my free time I'm designing an artillery warfare game called Staker (inspired by the old BASIC games Tank Wars and Scorched Earth) and I'm programming it in MATLAB. Your first thought might be "Why MATLAB? There are plenty of other languages/software packages that are better for game design." And you would be right. However, I'm a dork and I'm interested in learning the nuts and bolts of how you would design a game from the ground up, so I don't necessarily want to use anything with prefab modules. Also, I've used MATLAB for years and I like the challenge of doing things with it that others haven't really tried to do.
Now to the problem at hand: I want to incorporate AI so that the player can go up against the computer. I've only just started thinking about how to design the algorithm to choose an azimuth angle, elevation angle, and projectile velocity to hit a target, and then adjust them each turn. I feel like maybe I've been overthinking the problem and trying to make the AI too complex at the outset, so I thought I'd pause and ask the community here for ideas about how they would design an algorithm.
Some specific questions:
Are there specific references for AI design that you would suggest I check out?
Would you design the AI players to vary in difficulty in a continuous manner (a difficulty of 0 (easy) to 1 (hard), all still using the same general algorithm) or would you design specific algorithms for a discrete number of AI players (like an easy enemy that fires in random directions or a hard enemy that is able to account for the effects of wind)?
What sorts of mathematical algorithms (pseudocode description) would you start with?
Some additional info: the model I use to simulate projectile motion incorporates fluid drag and the effect of wind. The "fluid" can be air or water. In air, the air density (and thus effect of drag) varies with height above the ground based on some simple atmospheric models. In water, the drag is so great that the projectile usually requires additional thrust. In other words, the projectile can be affected by forces other than just gravity.
In a real artillery situation all these factors would be handled either with formulas or simply brute-force simulation: Fire an electronic shell, apply all relevant forces and see where it lands. Adjust and try again until the electronic shell hits the target. Now you have your numbers to send to the gun.
Given the complexity of the situation I doubt there is any answer better than the brute-force one. While you could precalculate a table of expected drag effects vs velocity I can't see it being worthwhile.
Of course a game where the AI dropped the first shell on your head every time wouldn't be interesting. Once you know the correct values you'll have to make the AI a lousy shot. Apply a random factor to the shot and then walk to towards the target--move it say 30+random(140)% towards the true target each time it shoots.
Edit:
I do agree with BCS's notion of improving it as time goes on. I said that but then changed my mind on how to write a bunch of it and then ended up forgetting to put it back in. The tougher it's supposed to be the smaller the random component should be.
Loren's brute force solution is appealing as because it would allow easy "Intelligence adjustments" by adding more iterations. Also the adjustment factors for the iteration could be part of the intelligence as some value will make it converge faster.
Also for the basic system (no drag, wind, etc) there is a closed form solution that can be derived from a basic physics text. I would make the first guess be that and then do one or more iteration per turn. You might want to try and come up with an empirical correction correlation to improve the first shot (something that will make the first shot distributions average be closer to correct)
Thanks Loren and BCS, I think you've hit upon an idea I was considering (which prompted question #2 above). The pseudocode for an AIs turn would look something like this:
nSims; % A variable storing the numbers of projectile simulations
% done per turn for the AI (i.e. difficulty)
prevParams; % A variable storing the previous shot parameters
prevResults; % A variable storing some measure of accuracy of the last shot
newParams = get_new_guess(prevParams,prevResults);
loop for nSims times,
newResults = simulate_projectile_flight(newParams);
newParams = get_new_guess(newParams,newResults);
end
fire_projectile(newParams);
In this case, the variable nSims is essentially a measure of "intelligence" for the AI. A "dumb" AI would have nSims=0, and would simply make a new guess each turn (based on results of the previous turn). A "smart" AI would refine its guess nSims times per turn by simulating the projectile flight.
Two more questions spring from this:
1) What goes into the function get_new_guess? How should I adjust the three shot parameters to minimize the distance to the target? For example, if a shot falls short of the target, you can try to get it closer by adjusting the elevation angle only, adjusting the projectile velocity only, or adjusting both of them together.
2) Should get_new_guess be the same for all AIs, with the nSims value being the only determiner of "intelligence"? Or should get_new_guess be dependent on another "intelligence" parameter (like guessAccuracy)?
A difference between artillery games and real artillery situations is that all sides have 100% information, and that there are typically more than 2 opponents.
As a result, your evaluation function should consider which opponent it would be more urgent to try and eliminate. For example, if I have an easy kill at 90%, but a 50% chance on someone who's trying to kill me and just missed two shots near me, it's more important to deal with that chance.
I think you would need some way of evaluating the risk everyone poses to you in terms of ammunition, location, activity, past history, etc.
I'm now addressing the response you posted:
While you have the general idea I don't believe your approach will be workable--it's going to converge way too fast even for a low value of nSims. I doubt you want more than one iteration of get_new_guess between shells and it very well might need some randomizing beyond that.
Even if you can use multiple iterations they wouldn't be good at making a continuously increasing difficulty as they will be big steps. It seems to me that difficulty must be handled by randomness.
First, get_initial_guess:
To start out I would have a table that divides the world up into zones--the higher the difficulty the more zones. The borders between these zones would have precalculated power for 45, 60 & 75 degrees. Do a test plot, if a shell smacks terrain try again at a higher angle--if 75 hits terrain use it anyway.
The initial shell should be fired at a random power between the values given for the low and high bounds.
Now, for get_new_guess:
Did the shell hit terrain? Increase the angle. I think there will be a constant ratio of how much power needs to be increased to maintain the same distance--you'll need to run tests on this.
Assuming it didn't smack a mountain, note if it's short or long. This gives you a bound. The new guess is somewhere between the two bounds (if you're missing a bound, use the value from the table in get_initial_guess in it's place.)
Note what percentage of the way between the low and high bound impact points the target is and choose a power that far between the low and high bound power.
This is probably far too accurate and will likely require some randomizing. I've changed my mind about adding a simple random %. Rather, multiple random numbers should be used to get a bell curve.
Another thought: Are we dealing with a system where only one shell is active at once? Long ago I implemented an artillery game where you had 5 barrels, each with a fixed reload time that was above the maximum possible flight time.
With that I found myself using a strategy of firing shells spread across the range between my current low bound and high bound. It's possible that being a mere human I wasn't using an optimal strategy, though--this was realtime, getting a round off as soon as the barrel was ready was more important than ensuring it was aimed as well as possible as it would converge quite fast, anyway. I would generally put a shell on target on the second salvo and the third would generally all be hits. (A kill required killing ALL pixels in the target.)
In an AI situation I would model both this and a strategy of holding back some of the barrels to fire more accurate rounds later. I would still fire a spread across the target range, the only question is whether I would use all barrels or not.
I have personally created such a system - for the web-game Zwok, using brute force. I fired lots of shots in random directions and recorded the best result. I wouldn't recommend doing it any other way as the difference between timesteps etc will give you unexpected results.