However, being extremely cautious is not the best idea in the long-term. I'm not suggesting that taking risks all the time is good, but I do advise taking at least one or two stupid gambles every game. Calculated risk-taking is important to victory. You can't be timid and let the enemy walk all over you, but you also can't be mindless. It's important to know the difference.
Following your heart is usually bad
Most people who play competitive games do so on pure instinct. The top players play largely on instinct, and the really awful players play 100% on instinct. What separates the good from the bad here is how good a player's instincts are. Unfortunately, you can't play with your heart and improve. You have to play with your head.
When you're a beginner, you don't really know what any of the commands do. You have to think about everything you do. You do things a lot more slowly. As you improve, more of the game gets deposited in your stored memory, and those things become natural. You no longer really have to think about which buttons to press.
Unfortunately, many people stop growing significantly as players shortly after that point. They start following whatever patterns they've developed over their games and don't really bother assessing (on a conscious level) whether those patterns are good or bad. When these players take risks, it's because they're tied to the game's positive feedback mechanism (e.g., getting kills), and it blinds them to the dangers involved.
When you actually go and do something stupid, you have to have full control of your logical brain and be ready to assess that you're taking a risk. After you've done it, you need to be able to verify logically whether your action was worth it. Did you accomplish anything? If so, what was the net gold exchanged on each team? If it was equal, did your team secure any additional objectives following your actions? How much time did you waste between you and the enemy? If you're not going to ask yourself those questions and be objective (and then type "worth it" in all chat), then don't take the risk.
On the flipside, though, being defensive is just another burned-in neural pathway, too. It's probably a better one overall, since it is less likely to throw the game for you. However, it's important that you not just play and expect to be better than your opponent.
If you are more aware of unusual scenarios, you are going to be more capable of leveraging them. If you have practiced level 2 or level 3 aggression in mid lane with your chosen character, you will know really well which situations are good and which ones are bad. You can learn that only if you try a lot. If you are conscious of when you hit level 3 and are aware that your character becomes very powerful when she has all three of her skills (hi, Riven), you can do reasonably well without knowing the exact matchup specifics. However, if you have practiced taking risks at level 3, you will learn over time which characters have answers to your aggression at that level, what those answers are, and how to bait them before you go all-in.
Additionally, if you practice those situations a lot and encounter an opponent who is unfamiliar with that kind of aggression, you can get ahead very early and win the game outright by yourself. It is very hard to win when one of your other lanes goes 0-5. If you practice that early aggression, you can make that happen more often than not.
Another important thing to do is turn around. If you're dead and you are running away on the tiny off chance that your opponent misclicks or something, do yourself a favor and learn to turn around. If you're already dead, the best thing you can do is go for it and try to deal some damage. If you learn the situations where you are 100% dead and just try to make the best of them, you'll help your team a lot in teamfights where that damage matters.
The bottom line with this is that learning things that make your opponent uncomfortable is worth taking risks, but remember the first part too -- you have to learn these things. Don't just go for broke every time. You need to mentally catalogue the results.