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These are the user uploaded subtitles that are being translated: 1 00:00:01,050 --> 00:00:03,770 Hello and welcome back to the course on artificial intelligence. 2 00:00:03,810 --> 00:00:08,280 And today we're talking about Mark of decision processes or M.D.. 3 00:00:08,760 --> 00:00:11,120 Let's have a look what we've got today. 4 00:00:11,430 --> 00:00:14,060 So last time we stopped on the concept of a map. 5 00:00:14,070 --> 00:00:19,980 So because we've calculated the values based on the Belman equation we can derive this map for our agent 6 00:00:20,010 --> 00:00:21,060 on this maze. 7 00:00:21,240 --> 00:00:27,570 And basically what that means is wherever the ange a agent starts let's say it starts over there. 8 00:00:27,570 --> 00:00:33,270 It knows exactly which steps to take in order to get to the finish line so it just goes up up right. 9 00:00:33,270 --> 00:00:35,040 Right and done. 10 00:00:35,070 --> 00:00:37,540 And so the question here is is that it. 11 00:00:37,590 --> 00:00:39,780 Is it really that simple. 12 00:00:39,780 --> 00:00:44,690 Is reinforcement learning really that you know for the lack of a better word boring. 13 00:00:44,790 --> 00:00:46,420 It's it's yeah. 14 00:00:46,440 --> 00:00:50,830 Once you have the math that's it all you have to do is you've done it just full of them. 15 00:00:51,090 --> 00:00:55,460 Well the reality is that it's not actually that simple. 16 00:00:55,500 --> 00:01:01,020 And that's a good thing because it makes this course more interesting for us and we can actually solve 17 00:01:01,020 --> 00:01:02,610 much more complex problems. 18 00:01:02,610 --> 00:01:05,460 So this is where a mark of a process is coming. 19 00:01:05,490 --> 00:01:07,770 But first we're going to talk about two things. 20 00:01:07,760 --> 00:01:11,450 We're into it deterministic search versus non-deterministic search. 21 00:01:11,700 --> 00:01:14,750 So let's talk about the concept of deterministic search. 22 00:01:14,820 --> 00:01:21,570 This is our agent in the maze and deterministic search means that if the agent decides to go up then 23 00:01:21,570 --> 00:01:26,980 what will happen is 100 percent probability it will go up. 24 00:01:27,030 --> 00:01:28,700 That's exactly what will happen. 25 00:01:28,700 --> 00:01:29,740 There's no other options. 26 00:01:29,740 --> 00:01:33,690 Once once it says go up or click the up arrow it'll go up. 27 00:01:33,690 --> 00:01:35,070 There's no other options. 28 00:01:35,250 --> 00:01:41,950 Now on the other hand nondeterministic search is when our agent says it wants to go up. 29 00:01:42,130 --> 00:01:44,430 They are actually couple of options. 30 00:01:44,460 --> 00:01:48,820 For example there could be three options and we're going to look an example where there are three options 31 00:01:48,830 --> 00:01:53,400 but it doesn't have to be a limit to three before it could be different depending on depends on the 32 00:01:53,400 --> 00:01:59,640 problem the randomness could be different but in our case it could be three options with an 80 percent 33 00:01:59,640 --> 00:02:01,640 chance he does go up. 34 00:02:01,860 --> 00:02:07,500 But then with a 10 percent chance when he wants to go up he'll actually go to the left just because. 35 00:02:07,500 --> 00:02:11,080 Because that's how the environment works that's the world that he lives in. 36 00:02:11,430 --> 00:02:14,840 And with another check in 10 percent chance he'll actually go right. 37 00:02:14,880 --> 00:02:17,770 And in this case he'll fall into the firepit. 38 00:02:17,850 --> 00:02:20,730 So that is how it all works. 39 00:02:20,760 --> 00:02:26,760 That's an example of a nondeterministic sure search a stochastic process and what the point of this 40 00:02:26,760 --> 00:02:35,370 is is to make a more realistic model of what could actually happen in a real world in a real world type 41 00:02:35,370 --> 00:02:40,560 of problem because very rarely do you get situations like this when you do something and it happens 42 00:02:40,560 --> 00:02:41,390 exactly that way. 43 00:02:41,520 --> 00:02:46,560 And even if you think about it in terms of games let's say you've got an agent playing Pac-Man. 44 00:02:46,740 --> 00:02:51,270 Well not always is it the case that if he's standing in the square he goes up. 45 00:02:51,360 --> 00:02:54,260 He will get the same exact result every time. 46 00:02:54,460 --> 00:02:59,820 Well he will indeed go up but it may be in one case you won't get eaten by a ghost in either case. 47 00:02:59,820 --> 00:03:01,570 He will get eaten by a ghost. 48 00:03:01,590 --> 00:03:05,970 So as you can see there's some randomness to it because it depends on how the ghosts are moving and 49 00:03:05,970 --> 00:03:07,350 they don't always move the same way. 50 00:03:07,350 --> 00:03:09,370 They don't always start in the same locations. 51 00:03:09,510 --> 00:03:16,140 So it's very logical is very fair that there is some randomness there's something that is not under 52 00:03:16,140 --> 00:03:21,810 the control of the agent and that is this is just a way for us to present that in order for us to learn 53 00:03:21,810 --> 00:03:27,240 how we can deal with it and how that affects a Belman equation how it affects the whole reinforcement 54 00:03:27,240 --> 00:03:29,010 learning process. 55 00:03:29,070 --> 00:03:33,780 But at the same time the randomness is of course not limited to if you go up there's a 10 percent chance 56 00:03:33,780 --> 00:03:38,400 you'll go right or temp's and just go left or if you go down to 10 percent chance you go right or left 57 00:03:38,400 --> 00:03:42,840 or you're right there's a 10 percent chance an up or down subtle limited to where you're going to end 58 00:03:42,840 --> 00:03:45,550 up sometimes you might have a problem that is exactly. 59 00:03:45,570 --> 00:03:47,390 Sometimes the possibilities might be different. 60 00:03:47,430 --> 00:03:52,990 Sometimes the randomness might boil down to something else it might be boiled down like that example. 61 00:03:52,980 --> 00:03:58,890 Pacman ghosts eating you are not eating you or it might boil down to something different. 62 00:03:58,890 --> 00:04:05,550 For instance like there's there's like if the agent is playing Doom and then there's something like 63 00:04:05,700 --> 00:04:11,040 a monster which is going to shoot him in one case and other cases there's like there's a probability 64 00:04:11,060 --> 00:04:14,380 if we should all get shot and we won't get shot. 65 00:04:14,550 --> 00:04:19,710 And so and so something that is out of the control of the agents is something I cannot predict. 66 00:04:19,710 --> 00:04:25,740 That's what we are modeling here in nondeterministic search and this is where we have directly approached 67 00:04:25,950 --> 00:04:32,780 two new concepts a mark of processes and or a mark of process and a marker mark of decision process 68 00:04:32,790 --> 00:04:34,130 so let's have a look at these. 69 00:04:34,150 --> 00:04:39,080 And you know how much I don't like to put definitions and lots of text on the side. 70 00:04:39,090 --> 00:04:42,280 But in this case it is necessary for us to go through that. 71 00:04:42,280 --> 00:04:46,220 So let's have a look a stochastic process has a mark of property. 72 00:04:46,240 --> 00:04:51,750 If the conditional probability distribution of future states of the process conditional and both past 73 00:04:51,750 --> 00:04:58,200 and present state depends only upon the present state not on the sequence of events that preceded it. 74 00:04:58,230 --> 00:05:00,410 A process with this property is called a marker. 75 00:05:01,040 --> 00:05:06,470 Very complex definition and it kind of like you introduce a little bit not only contradicts itself but 76 00:05:06,470 --> 00:05:11,110 feels like it contradicts itself so here it is conditional for positive presence that depends on your 77 00:05:11,110 --> 00:05:11,450 point. 78 00:05:11,480 --> 00:05:14,450 But at the same time it only depends upon the present state. 79 00:05:14,510 --> 00:05:17,510 So don't get too bogged down in that. 80 00:05:17,670 --> 00:05:23,050 I'll I'll break it down in simple terms so a mark of property is when your future states. 81 00:05:23,060 --> 00:05:25,310 So not just your choice but the whole thing. 82 00:05:25,310 --> 00:05:31,640 Your choice and the environment it will only like the results of all of the of the action you take in 83 00:05:31,640 --> 00:05:33,900 that environment will only depend on where you are now. 84 00:05:33,920 --> 00:05:35,770 It will not depend on how you got there. 85 00:05:36,110 --> 00:05:36,560 And that's it. 86 00:05:36,560 --> 00:05:40,630 So that's a matter of public and a process which has this property is called the market process. 87 00:05:40,880 --> 00:05:47,570 So to put it into an example so if your agent is here and if he goes if he decides to go up he might 88 00:05:47,570 --> 00:05:48,030 go. 89 00:05:48,040 --> 00:05:52,940 He in our case in our nondeterministic search example he actually might go left and right. 90 00:05:53,000 --> 00:05:53,680 All right. 91 00:05:53,690 --> 00:05:58,940 That's because we have that stick a this city inside our environment we have that randomness inside 92 00:05:58,940 --> 00:05:59,710 our environment. 93 00:05:59,810 --> 00:06:01,820 So any one of these things might happen. 94 00:06:01,820 --> 00:06:07,250 But the key here is that this is a mark of process because we don't care how you got here. 95 00:06:07,250 --> 00:06:10,700 He could have come from the top ended up here he could have come from the left and that up here you 96 00:06:10,700 --> 00:06:12,370 could come from the bottom and end up here. 97 00:06:12,380 --> 00:06:16,640 He could have like play a moved around here like 100000 times and then got here. 98 00:06:16,700 --> 00:06:22,490 It does not matter what happened before only what matters is which state is he in now. 99 00:06:22,520 --> 00:06:31,160 And so the the probabilities of going left or right or up they will always be the same if he's in this 100 00:06:31,160 --> 00:06:32,250 state now. 101 00:06:32,690 --> 00:06:37,530 And so that's basically just saying it doesn't matter what happened before we're here now. 102 00:06:37,640 --> 00:06:39,150 This is the state you're in. 103 00:06:39,200 --> 00:06:42,320 And don't forget that state doesn't just mean where he's standing. 104 00:06:42,320 --> 00:06:48,140 The state is the state of the whole of the whole of the agent in the environment so is there like monsters 105 00:06:48,140 --> 00:06:53,030 on the right or the monsters on the left or you know is the ghost coming from a top or bottom whatever 106 00:06:53,090 --> 00:06:54,530 state you're in now. 107 00:06:54,560 --> 00:06:58,460 Doesn't matter how you got there doesn't matter how and how it all came to be that you're there in that 108 00:06:58,460 --> 00:06:58,790 state. 109 00:06:58,790 --> 00:07:02,990 Now what will happen in the future is only determined by the state you're in now. 110 00:07:02,990 --> 00:07:07,440 Plus the actions you will take them plus of course the randomness that is overlaid on top of that. 111 00:07:07,460 --> 00:07:14,280 So that's a mark of process and a marker decision process or an MVP or marker decision process. 112 00:07:14,390 --> 00:07:20,390 Provide a mathematical framework for of modeling decision making in situations where outcomes are partly 113 00:07:20,420 --> 00:07:23,430 random and partly under control over decision making. 114 00:07:23,570 --> 00:07:29,120 So important to understand that mark of decision process processes are different and different whole 115 00:07:29,150 --> 00:07:32,210 concept mark of process to mark of process. 116 00:07:32,340 --> 00:07:34,810 There are like a mathematical framework so. 117 00:07:34,970 --> 00:07:39,080 But at the same time I thought it was important for us to understand what a mark of process is because 118 00:07:39,170 --> 00:07:45,140 I think it still helps in understanding of mark mark of decision process and so a mark of decision process 119 00:07:45,200 --> 00:07:46,130 is there. 120 00:07:46,230 --> 00:07:50,950 This is exactly what we've been discussing Up till now so that the agent lives in this environment where 121 00:07:51,290 --> 00:07:56,570 he has control like him previously and had full control of what's going on but now it has a little bit 122 00:07:56,570 --> 00:07:57,530 less control. 123 00:07:57,590 --> 00:08:00,270 It can decide to go up but it actually knows. 124 00:08:00,290 --> 00:08:05,570 OK so if I go up there's an apes chance I'll go up this attempts and chances go left and chance will 125 00:08:05,560 --> 00:08:06,170 go right. 126 00:08:06,170 --> 00:08:08,930 So not everything is fully under its control. 127 00:08:08,930 --> 00:08:13,280 There is some randomness in this environment and that's exactly what a mark of decision process and 128 00:08:13,280 --> 00:08:18,830 Markov decision process is the framework that the agent will use in order to understand what to do in 129 00:08:18,830 --> 00:08:19,400 this environment. 130 00:08:19,400 --> 00:08:22,400 So we've got an environment with some toxicity some randomness. 131 00:08:22,550 --> 00:08:27,000 And now the agent has to choose for instance should go up down left or right. 132 00:08:27,370 --> 00:08:28,530 He has to make that decision. 133 00:08:28,520 --> 00:08:29,820 He doesn't know what to do. 134 00:08:30,140 --> 00:08:36,200 And in order to make that decision is going to apply a framework is going to be using a mark of decision 135 00:08:36,200 --> 00:08:40,960 process in order to make that decision what what's going to happen where it's going to go. 136 00:08:40,970 --> 00:08:47,600 And so basically this environment that poses this problem it is referred to the mark of decision process 137 00:08:47,600 --> 00:08:52,820 so it's the framework the agent using at the same time the environment is referred to that the agent 138 00:08:52,820 --> 00:08:55,810 is operating in a market decision process environment. 139 00:08:56,280 --> 00:09:01,190 And so basically here we have two concepts we've got the mark of process is the way this environment 140 00:09:01,190 --> 00:09:03,740 is designed that the PA does the work. 141 00:09:03,770 --> 00:09:07,020 What happens from where you are now doesn't depend on the past. 142 00:09:07,130 --> 00:09:11,240 And that same time we've got the mark of decision process is the framework that the agent is going to 143 00:09:11,240 --> 00:09:13,630 be using in order to solve this environment. 144 00:09:13,970 --> 00:09:18,830 And the good news is that the mark of decision process or that framework that we're talking about is 145 00:09:18,830 --> 00:09:24,730 actually just an add on to our Belman equation question is the Belman equation but just a bit more sophisticated. 146 00:09:24,740 --> 00:09:26,960 So let's have a look at that. 147 00:09:27,050 --> 00:09:28,910 This is our Belman equation so far. 148 00:09:29,030 --> 00:09:31,030 It's the maximum of all possible actions. 149 00:09:31,040 --> 00:09:35,150 So the value of being in a state is the maximum of all possible actions that you can take from that 150 00:09:35,150 --> 00:09:35,990 state. 151 00:09:36,260 --> 00:09:41,930 The maximum is taken from the reward that you would get by taking that action in that state plus a discount 152 00:09:41,930 --> 00:09:45,410 factor times the value of the next state which is as prime. 153 00:09:45,410 --> 00:09:47,390 So that's what we've had so far. 154 00:09:47,400 --> 00:09:52,550 Now because we have some randomness in our whole process this this part will change because we don't 155 00:09:52,550 --> 00:09:57,620 actually know which state will end up and we don't know what s prime will be will it be if we're going 156 00:09:57,630 --> 00:10:03,680 up will it be up or will be left will be right so we actually have to place this with the expected value 157 00:10:03,680 --> 00:10:04,960 of the next date. 158 00:10:04,970 --> 00:10:08,810 So here we're going to replace this so there's three possible states we can end up in. 159 00:10:08,810 --> 00:10:15,480 And so we're going to replace that with some value that state has a value of as one prime. 160 00:10:15,520 --> 00:10:18,190 That it has a view of as prime to prime. 161 00:10:18,470 --> 00:10:22,490 And this state has a value of the of us three Bryne. 162 00:10:22,640 --> 00:10:28,790 So now we're going to multiply the state that we actually are intending to go into by 80 percent because 163 00:10:28,790 --> 00:10:33,770 that's how probability of getting to that state plus the probability of getting to this state is 10 164 00:10:33,770 --> 00:10:39,800 percent plus people getting in-state So this is just our expected value so if from statistics if we 165 00:10:39,800 --> 00:10:46,880 take the expected value of getting into the state that we'll get into these are kind of like the average 166 00:10:47,060 --> 00:10:52,040 What's the average of what we'll get and then we replace that over here. 167 00:10:52,040 --> 00:10:56,210 Then we get this aggression and it jumps very quickly just because there's a big but if you look at 168 00:10:56,210 --> 00:10:59,930 it carefully you'll see the same thing said about Max here Max here. 169 00:10:59,960 --> 00:11:06,340 Then you've got r of S and A R of S and they you've got gamma you've got gamma. 170 00:11:06,410 --> 00:11:08,600 And then finally here you've got v. 171 00:11:08,630 --> 00:11:13,640 So you knew exactly it was a deterministic search you knew which states you'll get into. 172 00:11:13,640 --> 00:11:16,120 Now you don't know which state you'll get into since that of taking V. 173 00:11:16,120 --> 00:11:23,300 You're taking the expected value of the state you'll get into or of the future state or just in simpler 174 00:11:23,300 --> 00:11:25,920 terms you're just taking the average of what you will getting into. 175 00:11:26,060 --> 00:11:32,450 So you know like it was like for 30 plus 3 percent chance it will be like this Plus's divide by three 176 00:11:32,590 --> 00:11:32,900 basically. 177 00:11:32,900 --> 00:11:37,130 But in this case it's not it's not exactly like average average. 178 00:11:37,130 --> 00:11:40,410 It's it's a weighted average because of the probabilities here. 179 00:11:40,430 --> 00:11:45,980 So here you've got the probability of it when you're in this stage to take this action of getting into 180 00:11:46,040 --> 00:11:50,630 state as prime time the value of s prime and some to cross all these primes that you could possibly 181 00:11:50,630 --> 00:11:51,830 get into who we are. 182 00:11:51,830 --> 00:11:54,690 So exactly what we had three here one two three. 183 00:11:54,890 --> 00:11:57,330 Add them up multiply these add them up. 184 00:11:57,330 --> 00:11:58,040 Same here. 185 00:11:58,040 --> 00:11:58,820 One two three. 186 00:11:58,820 --> 00:12:01,660 Multiply them by the probabilities and add them up. 187 00:12:02,090 --> 00:12:05,180 And that is your new Belman equation. 188 00:12:05,180 --> 00:12:06,440 Congratulations. 189 00:12:06,470 --> 00:12:08,990 This is what we're going to be working with going forward. 190 00:12:09,140 --> 00:12:15,590 And that is the framework that is used in of decision processes so that is the framework that solves 191 00:12:15,590 --> 00:12:16,490 this. 192 00:12:16,620 --> 00:12:22,670 That agents used to solve this whole stochastic nondeterministic search problem where there's random 193 00:12:22,670 --> 00:12:25,460 events that are happening that they cannot control. 194 00:12:25,460 --> 00:12:26,920 So it's it's much more complex. 195 00:12:26,930 --> 00:12:30,150 But as you can see because we've built up slowly to it. 196 00:12:30,290 --> 00:12:33,120 Now we already know about this we know about. 197 00:12:33,130 --> 00:12:35,090 There's worry about this. 198 00:12:35,090 --> 00:12:36,160 We know about this. 199 00:12:36,170 --> 00:12:36,710 We know what they are. 200 00:12:36,710 --> 00:12:42,500 So all we did is we just introduced this part over here because there are probabilities involved in 201 00:12:42,920 --> 00:12:49,000 the action or the consequences of your action on nondeterministic they are based on probabilities. 202 00:12:49,220 --> 00:12:50,600 And so there we go. 203 00:12:50,600 --> 00:12:58,280 That's how a marker of decision process works and the underlying equation behind it. 204 00:12:58,330 --> 00:13:04,630 Once again it is something that is more like more closely resembles real world problems real or Sinatras 205 00:13:04,670 --> 00:13:08,690 or even game scenarios because not everything is straightforward. 206 00:13:08,690 --> 00:13:15,880 There is some randomness of all involved and not always will taking an action in a certain state will 207 00:13:15,870 --> 00:13:18,810 always Nawal not always will it lead to the same outcome. 208 00:13:18,890 --> 00:13:23,150 And so this is what we're going to be dealing with going forward and that's going to make things way 209 00:13:23,150 --> 00:13:24,310 more interesting. 210 00:13:24,380 --> 00:13:29,290 So hopefully you're excited for that and excited to see what's going to come next. 211 00:13:29,690 --> 00:13:35,870 And in the meantime I found a really cool paper for you to have a look at this time. 212 00:13:35,870 --> 00:13:37,460 It's a very applied paper. 213 00:13:37,460 --> 00:13:40,150 So this one is actually really interesting to read through. 214 00:13:40,160 --> 00:13:46,810 It's called a survey of applications of Mark of decision processes proces and it was written by white 215 00:13:46,820 --> 00:13:47,970 in 1993. 216 00:13:47,990 --> 00:13:56,000 There's the link and Ill show you examples of where Markov decision processes actually are used to model 217 00:13:56,000 --> 00:13:59,560 real life Sinatras I think I was very excited by this. 218 00:13:59,560 --> 00:14:03,880 I was impressed by some examples of population harvesting for instance. 219 00:14:03,880 --> 00:14:09,290 So let's say you have some fish and you know what the population of fish is you need to decide how many 220 00:14:09,290 --> 00:14:12,910 fish can we fish out this year and what. 221 00:14:13,250 --> 00:14:14,330 So that's your current state. 222 00:14:14,330 --> 00:14:17,220 That's the action that you're taking How many can we've shot at this year. 223 00:14:17,230 --> 00:14:20,420 So what are the up what are the possible outcomes of that. 224 00:14:20,540 --> 00:14:22,100 How many fish will we have next year. 225 00:14:22,160 --> 00:14:25,210 How many fish will we have the year after and the year after and so on. 226 00:14:25,250 --> 00:14:30,230 And it's not deterministic because it's not like if you take it at an hour and 90 percent of the population 227 00:14:30,230 --> 00:14:34,640 the next year you will have you know back to 100 percent is not not exactly sermonising. 228 00:14:34,640 --> 00:14:39,590 There are certain random factors involved which are out of our control and therefore we have to understand 229 00:14:39,760 --> 00:14:43,640 what's what's going to happen we have to model what's going to happen that's where a market decision 230 00:14:43,860 --> 00:14:46,060 processes agriculture. 231 00:14:46,070 --> 00:14:50,250 There's an example like something like harvesting crops how much crops do we harvest how much money 232 00:14:50,280 --> 00:14:51,440 do we not harvest. 233 00:14:51,470 --> 00:14:58,190 Another one which I looked at finance and investment like an insurance company needs to decide how much 234 00:14:58,190 --> 00:15:04,990 of its funds it will invest in any I think day or year or some period of time and there are those certain 235 00:15:05,020 --> 00:15:06,490 factors are of his control. 236 00:15:06,490 --> 00:15:11,260 For instance you know the market movements it doesn't know what can happen so it needs to actually model 237 00:15:11,260 --> 00:15:12,070 that somehow. 238 00:15:12,110 --> 00:15:14,350 A mark of decision processes used for that. 239 00:15:14,350 --> 00:15:16,890 So here you can see lots and lots of examples. 240 00:15:16,900 --> 00:15:20,340 And this is the number of examples given I think for each one. 241 00:15:20,650 --> 00:15:28,030 And so you know even sports examples for sports and epidemics and motor insurance claims inspections 242 00:15:28,090 --> 00:15:31,030 and maintenance and repairs it's also very interesting. 243 00:15:31,030 --> 00:15:31,900 Have a look at that. 244 00:15:31,930 --> 00:15:40,390 Just to give you an understanding of hey this is not just all made up stuff hypothetical The Matrix 245 00:15:40,390 --> 00:15:41,130 type of thing. 246 00:15:41,140 --> 00:15:45,580 This is actually the real world scenario so Ill give you a better understanding and this is what we 247 00:15:45,580 --> 00:15:50,410 talked about in the promotional video for the scores that or the description of the course that we're 248 00:15:50,410 --> 00:15:55,900 going to inspire you and your intuition to give you ideas for how to use AI in real life. 249 00:15:55,900 --> 00:15:57,820 This is your opportunity. 250 00:15:57,820 --> 00:15:59,790 Look at this paper to understand. 251 00:15:59,900 --> 00:16:02,890 OK so we're going to be dealing with mark of decision process going forward. 252 00:16:02,890 --> 00:16:07,210 That's really cool what do they look like in real life and this possibly could trigger some ideas for 253 00:16:07,210 --> 00:16:13,300 you how you could apply in the future to make the world a better place and we'd be super happy about 254 00:16:13,300 --> 00:16:13,650 that. 255 00:16:13,690 --> 00:16:18,560 We'd be happy if you could use what you learn in this course to make the world a better place. 256 00:16:18,730 --> 00:16:20,050 How fantastic with that. 257 00:16:20,380 --> 00:16:23,170 So on that note I hope you enjoyed today's tutorial. 258 00:16:23,170 --> 00:16:24,540 I look forward See you next time. 259 00:16:24,610 --> 00:16:26,420 And until then enjoy AI. 28357